An open-access market for global communications ☆

An open-access market design is presented to manage network congestion and optimize network use and value. Open access eliminates the walled-garden approach; instead, it commoditizes communications network capacity while decentralizing access to a transparent wholesale market. It ensures that scarce capacity is put to its best use by providing a platform for efficient trade. The market operates without friction using flow trading. It allows participants to bid persistent piecewise-linear downward-sloping demand curves for portfolios of products, gradually adjusting positions toward targeted needs. Flow trading allows fine granularity of products in time and location, creating complete markets. Liquidity and computational feasibility are maintained despite trading millions of interrelated forward and real-time products. Participants manage risk and adverse price impact through trade-to-target strategies. The market operator clears the market every hour, finding unique prices and quantities that maximize as-bid social welfare. Prices, aggregate quantities, and the slope of the aggregate net demand are public. The market operator observes positions, enabling it to optimize collateral requirements to minimize default risk. Priority pricing is used to manage real-time imbalances. An application of the model is developed for intersatellite wholesale communications with optical (laser-beamed) mesh networks in space, showing several efficiency gains.


Introduction
While many communications markets are open to competition, they remain highly concentrated, with significant barriers to entry.Market forces push mobile network operators to consolidate from four to three in many markets and three to two in others.Fixed broadband options often are limited to one or two providers.
Limited competition should not come as a surprise given the considerable fixed cost of building a network.The communications industry quickly consolidated into a "natural" monopoly in the early years of the telephone.Technology advancements have made the monopoly model obsolete, but high fixed costs still limit competition.This is especially true when dominant incumbents have incentives to discourage competition, as the US history of "Ma Bell" illustrates.The Bell System worked to preserve and extend its monopoly into any device that touched its network.Bell's behavior eventually led to antitrust lawsuits in the 1970s and Bell's breakup in the 1980s.The history is similar in other countries (Cave et al., 2019).The road to competitive communications markets is a long one made longer by the actions of dominant incumbents.
Despite open architectures like the internet and the regulated connections between networks (a customer on one network talking with a customer on another), each network is its own walled garden with the network owner as the "chief gardener" in charge of access. 1 Often, that network owner sells connectivity on the network to businesses or other service providers through bilateral transactions.The product offered is dedicated connectivity of opaque quality with static pricing, whether a fixed fee, a per-gigabyte fee, or some combination.These bilateral deals create walled gardens within the network owner's walled garden.Idle network capacity results in an illusion of scarcity.Value is lost behind the garden walls.Innovation and competition are stifled.Instead of driving value by enabling people and their creativity, the paradigm strands potential.
This paper proposes an open access wholesale market that eliminates walled gardens, building on recent advances in wholesale electricity markets (Cramton et al., 2024). 2 The wholesale market includes a real-time market and a forward market.The open-access market operates without friction using flow trading (Budish et al., 2023).Participants bid persistent piecewise-linear downward-sloping net demand curves for portfolios of products.A market operator may be designated by the market players as an independent trading platform, even if the market structure is characterized as an oligopoly.Doing this facilitates network utilization and network rents.
We consider a neutral wholesale network operator that conducts the market to maximize as-bid social welfare.The market rules unambiguously define what is meant by maximizing as-bid social welfare.As-bid means that welfare is optimized with respect to the bids.The market rules state the form of bid expression and the precise optimization that translates bids into prices and quantities.The designated market operator clears the market every hour, finding unique welfare-maximizing prices and quantities.Prices, aggregate quantities, and the slope of the aggregate net demand are made public.The market operator observes positions, enabling it to optimize collateral requirements to minimize default risk.
This open-access market model is applied to intersatellite communication via lasers.A laser-equipped low-earth-orbit mesh network can provide global broadband communications independent of terrestrial fiber networks.Benefits of the technology include 1) global connectivity, 2) low latency since the communications travel 50 percent faster through the atmosphere (299,792 km/s) than fiber (200,000 km/s), and 3) optimized, internet-independent routing for improved latency, reliability, and security.This open-access market complements the rise in broadband satellite competition and terrestrial and satellite communications convergence.However, satellite networks come with one limitation.Capacity is much more constrained than terrestrial fiber networks.The limiting factor is earth-satellite throughput; satellite-to-satellite laser throughput is not expected to be an additional bottleneck (laser throughput is between 20 and 100 Gbps).Maximum earth-satellite throughput varies by satellite and atmospheric conditions.A state-of-the-art fiber cable has a throughput of 100,000 Gbps, several orders of magnitude more than earth-satellite throughput.While capacity constraints arise in terrestrial communications networks, network congestion is much more severe for satellite communications, so its management is critical.Revenue management is also essential given the large network-deployment fixed costs.With open access, revenue management is addressed with the supplier offering supply at prices that exceed marginal cost, much as an airline offers seats, especially in premium classes, at prices above marginal cost.This paper addresses the emerging intersatellite communication market by developing an open access model.
Developing an open-access market would be irrelevant if no supplier had an incentive to adopt it.We argue that adopting and committing to the open-access market serves a supplier's (satellite provider's) interest.Doing so maximizes the network's value so long as the communications market is competitive on the buy side.There are many communications buyers; even the largest buyer purchases a small fraction of the total capacity.Each supplier has an interest in maximizing the value its supply brings to buyers.The open access market creates value by managing congestion efficiently, instead of rationing quantity.
Questions can be raised about whether a satellite provider can be expected to commit to an open-access market.The key is the delegation of network operation to an operator whose mission is open access and who is constrained to operate under the open access rules.This is practically accomplished with governance rules that make it difficult to alter the core tenets of open access.Commitments of this sort are commonplace and especially easy to enforce when the tenets are broadly consistent with the supplier's interests, such as trading platforms in financial markets.We view this as a reasonable assumption, and with this, the oligopoly structure of the satellite supply side is irrelevant.
Our methodology is market design.We start with the market's objective and recognize the potential market failures that must be mitigated to achieve the objective.Unlike mechanism design (Myerson, 2008) and industrial organization theory (Tirole, 2015), which are mathematical tools to characterize theoretical possibilities within an assumed structure, market design is pragmatic and focused on implementation (Chen et al., 2021;Cramton, 2009;Milgrom, 2004;Roth, 2002).We define market rules and a means of preference expression, typically a bidding language, that provides participants with good incentives.The market design approach maximizes "asbid" social welfare, recognizing that truthful bidding is only an approximation.We sacrifice rigorous welfare theorems and instead are 1 The height of the garden walls varies among countries, depending primarily on regulatory decisions and the legal framework.For example, European mobile communications are closer to open access than North America.Europe's "roam like your home" policy is the best example.
2 The day-ahead and real-time markets of US wholesale electricity markets successfully illustrate the open-access approach described here.Both markets have rich time and location granularity with tens of thousands of interrelated products that simultaneously clear.Market operators are responsible for maximizing social value, and some markets utilize a version of flow trading, Cramton (2017); Cramton and Ockenfels (2024).
P. Cramton et al. content with a market that works well in practice. 3 The paper presents a market design for an open access global communications market.It starts by discussing satellite networks, the market structure, and the open access innovation.Objectives and the benefits of the open-access approach are discussed.The market participants, governance, the role of forward trading, and the distinction between real-time and forward trading are examined.An outline of the market rules, the granularity of products, and the approach to efficient trade are discussed.The simplicity of participation in a market with fine product granularity is explained.Before concluding, the paper discusses liquidity, counterparty risk, flexibility, and competition.

Satellite global networks
Space-based optical mesh networks offer high-performing global communications.At least three networks are proposed with intersatellite laser technology: 1) Amazon, 2) Starlink, and 3) Rivada.Starlink performed successful tests in September 2023; Amazon had successful tests in November 2023; Rivada plans its first launch in 2024.There are essential differences between these constellations: Starlink and Amazon are internet service providers, connecting an end-user's dish at one end to an internet gateway.They are using laser links to extend the distance from the gateway from which they can offer service.In contrast, Rivada's planned optical mesh network is currently the only one designed to route traffic across its constellation from end to end.It is not intended to provide consumer-grade internet access.Rather, it is to function as an internet backbone in space-an Outernet.
These differences are important.If the Rivada model proves successful, then we would expect others to move in this direction.Laser-linked low-earth-orbit constellations will evolve in the direction of true orbital mesh networks over time.Low-earth-orbit architectures have three classifications.A Type I constellation like Starlink's current offering provides a last-mile gateway.The satellite is used only for earth-satellite-earth communications to expand connectivity to remote locations.All traffic is routed to the nearest internet gateway.A Type II constellation like Amazon's offering and Starlink's next-generation offering provides last-mile connectivity with a laser extension.Earth-satellite-satellite-earth communication is possible, expanding the reach of satellite connections.A type III constellation like Rivada is developing is a true meshed multiprotocol-label-switching network in space.This approach enables end-toend connectivity over the satellite network with optimized routing and full global reach.
Amazon and Starlink focus primarily on the retail consumer market.Rivada concentrates on government and enterprise communications.The retail focus requires much greater capacity, resulting in many more individual users and endpoints on the network.This is one reason that Amazon and Starlink have many more satellites than the smaller Rivada network, which has a smaller number of larger, more capable satellites designed to serve a smaller population of user terminals.The three networks also differ in satellite altitude.Amazon is 610 km above sea level, Starlink is 570 km, and Rivada is 1052 km.A higher altitude implies marginally longer earth-satellite latency, greater visibility, and potentially fewer satellite-satellite hops.See (Pachler et al., 2021) for a detailed capacity estimate based on January 2021 FCC filings.Fiber dominates optical mesh networks in terms of capacity.For densely populated areas, fiber is the preferred choice, at least if the communications are traveling a distance of a few thousand kilometers or less.
Despite these capacity constraints, optical mesh networks in orbit will be critical in meeting burgeoning connectivity demand.First, they provide critical redundancy.When there are power outages, fiber and cellular networks become unreliable.The ground networks often have inadequate backup power.For critical communications, an optical mesh network provides a fallback.All that is needed is battery backup for the receiver and router.Critical communications can continue uninterrupted.Modern routers, such as Eero, automatically switch to backup internet.
Second, optical mesh networks in orbit have a latency advantage for communications over several thousand kilometers or more.Latency-critical applications such as high-frequency trading benefit from low latency.High-frequency traders are in an arms race for speed.The fastest trader gets to pick off stale quotes when market fundamentals change; speed is essential (Budish et al., 2015).Table 1 Theorem 2 gives the distance between the top ten global financial centers.Many are separated by several thousand kilometers.
Tables 2 and 3 show the millisecond time between any pair of top-ten financial centers via optical mesh network or terrestrial fiber.The optical mesh network assumes an additional distance to and from the low-earth-orbit satellite, which takes 7 ms for Rivada (the Amazon and Starlink roundtrip takes about 4 ms).The communications travel near the speed of light in a vacuum (299,792 km/s).The communications in the terrestrial fiber network travel at the speed of light in glass (about 200,000 km/s), two-thirds of the speed in air, due to glass's much lower refractive index.
Table 4 takes the difference between Tables 3 and 2 to yield the time savings of the optical mesh network in orbit.This calculation assumes a straight-line approximation between cities and ignores the number of hops required.The terrestrial fiber network will involve a less straight route and more hops, so these are conservative assumptions.For example, communication between New York and Tokyo can occur with about four hops and a direct polar route in an optical mesh network, such as NY to NY-satellite to North Polesatellite to Tokyo-satellite to Tokyo.Standard communications may involve more hops and longer latency.
Table 5 summarizes the magnitude of the time savings between each city pair.Over three-quarters of the city pairs have a significant improvement in latency.One millisecond is an eternity for a high-frequency trader.Other communications applications, such as online gaming and video conferencing, also benefit from low latency.Low latency is an essential quality attribute for a segment of demand.
A third and transformative benefit of an optical mesh network is coverage.The supplier's low-earth-orbit constellation can connect 3 By contrast, mechanism design would make theoretical assumptions and then identify incentive-compatible mechanisms that guarantee truthful bidding is consistent with equilibrium behavior in the assumed framework.
P. Cramton et al. two global points at gigabit speeds, with low latency and unmatched security.Typically, each satellite is equipped with four laser intersatellite terminals.The four lasers weave together a mesh network that encircles the globe, enabling direct connections between any point in the space-based network with terrestrial terminals.This separation will improve cyber security and data sovereignty by avoiding terrestrial internet gateways, a critical requirement for many government and enterprise uses.Multiple satellite networks at

Table 1
Distance between the top-ten global financial centers in kilometers.

Table 2
Communication time (ms) between the top-ten financial centers via optical mesh network.

Table 3
Communication time (ms) between the top-ten financial centers via terrestrial fiber network.
P. Cramton et al. different altitudes provide valuable redundancy, improving resilience to terrestrial and space threats.Three proposed optical mesh networks are shown in Table 6.Each differs in altitude-distance from earth-and the number of satellites.Starlink is the most ambitious, with a plan for 42,000 satellites; the table uses 10,000 as a more realistic number for the near term.A lower altitude is preferred for denser networks, improving communication latency over a shorter distance.For example, the straight-line no-hop latency between New York and Los Angeles is 17 ms with Amazon's and Starlink's constellations and 20 ms for Rivada's, slightly faster than terrestrial fiber.Terrestrial fiber dominates for shorter distances, such as New York to Chicago, although terrestrial microwave links are the fastest.For longer distances, such as New York to Tokyo, Rivada's network dominates because the higher altitude reduces the required hops.
The critical limitation of the optical mesh networks is capacity.Optimized routing and pricing are used to manage congestion and maximize capacity.To date, Starlink has relied on traditional static pricing.Rivada plans to incorporate dynamic congestion pricing via an open-access market.Other networks may shift to dynamic pricing, as the efficiency gains are too significant to ignore.However, both Amazon and Starlink are focused on retail broadband, a sector where static pricing and rationing are acceptable.The primary retail use is video streaming, where rationing works reasonably well.Consumers can accept a degradation of video quality from UHD to HD when data rates are limited, and buffers can smooth short-duration congestion.By contrast, when committed to the more demanding requirements of business-to-business and government applications, like Rivada, efficient routing and pricing become essential.

Market structure
The economics of optical mesh networks is different from terrestrial fiber.Fiber is a natural monopoly.The dominant expense is laying cable.Once a line is installed, a competing cable is redundant.Despite its capacity virtues, fiber is very expensive to lay.A fiber network covering 80 percent of the US population would cost hundreds of billions of dollars.Only a minority of the global population will be served by fiber.
In contrast, an optical mesh network covering every point on earth can be built for less than 10 billion dollars.The main cost is building and orbiting the satellites.Thus, economies of scale are modest, and building an optical mesh network with twice the capacity costs twice as much.The absence of economies of scale beyond about $5 billion means that the initial entrant, Starlink, cannot deter the entry of others. 4wo other fundamental economic trends support the expansion of optical mesh networking in orbit.Launch costs are declining quickly, thanks in no small part to SpaceX, but supported further by other new commercial entrants into a satellite-launch market that

Table 4
Communication time savings in milliseconds of optical mesh network.

Table 5
Optical mesh network time savings (ms) between each of the top-ten global financial centers.state actors had formerly dominated.Satellite mass manufacturing is finally coming into its own, promising a future in which modular, mechanized, and cost-effective assembly-line techniques and 3-D printing replace bespoke and costly manufacturing.These market changes are driving down the still-high up-front costs of establishing space-based networks, and so, in turn, improving the economics of adding capacity in orbit.
Expanding penetration also supports entry.Demand for communications has increased as technological advances create new datahungry applications.Moreover, as these technologies become more powerful, the adoption rates increase.Telephone penetration never exceeded 20 percent.By contrast, mobile phone penetration is 100 percent, and broadband internet penetration is 60 percent and rising.See Fig. 1.
Demand for communications varies by time and place.People are dispersed unequally around the globe, as shown in Fig. 2.More granular depictions of population density would show more heterogeneity.Most people live in densely populated urban areas, concentrating communications demand.By contrast, the supply of satellite communications is distributed much more uniformly globally.Thus, to balance supply and demand, the price of satellite communications must vary by location.Satellite networks need dynamic pricing to balance supply and demand.
Communication demands also vary by time of day and day of week.With static pricing, time-of-use variability is managed with quality reductions.Users may experience poor availability and throughput at peak times.With dynamic pricing, price balances supply and demand, increasing availability and throughput for those users who demand good performance.The customer gets to decide the desired quality of service and is motivated to shift non-urgent communications to periods of lower demand.
Variations of demand over time and place and a constant supply dictate that prices must vary by time and place to balance supply and demand.The alternative is to ration demand during peak periods.Rationing is tolerable only if capacity is rarely constrained.However, the limited capacity of satellite communications implies a need for dynamic pricing (Bobbio et al., 2023).This need is the motivation for the open-access market.

The open-access market innovation
The open-access market rests on the principle of efficient pricing.A designated market operator conducts an open-access marketplace that brings fairness, transparency, and ease of access to customers who want to acquire network capacity.A network supplier offers wholesale capacity to customers, primarily governments, multinational enterprises, and communications service providers, including mobile network operators and mobile virtual network operators.Customers can purchase or sell capacity in realtime or on a forward basis, as overseen by the market operator, offering flexibility and the ability to manage risk.
The open-access market is a fundamental shift from connectivity (Mbps) by contract to capacity (GB) on demand when and where needed.Customers will actively influence the wholesale market's design and mechanisms through a dispersed governance structure motivated to optimize the market's performance through continuous improvement.The open-access, dynamically-priced market will spur competition in communications services globally and decentralize the innovative power of those services.This highly efficient market will maximize the network's and its users' potential, with benefits to social and economic development and global security.
Below find more details on the market's objectives, benefits, and operations.For concreteness, this paper presents a blockchain implementation of the primary market, as developed by Rivada, although a traditional implementation works similarly.

Objectives of the open-access market
The open-access market derives from basic economic principles.Anyone can participate in the market on open, nondiscriminatory terms.Scarce resources are efficiently priced to balance supply and demand. 5Open access has four principal objectives.
Efficiency.Open access drives more efficient use of network resources, maximizing value through a dynamic pricing mechanism of a

Table 6
Coverage area of a satellite constellation by altitude.
commoditized unit of network capacity.Market participants can buy or sell capacity on demand in real-time or through a forward market pursuant to their forecasted needs.
Fairness.Open access eliminates discriminatory barriers, providing equal opportunity for everyone to enter the market and buy and sell capacity.The market is indifferent to how the network is used, whether in enterprise applications, competitive wireless or wireline communications, or whether it is resold.
Transparency.Units of network capacity are represented in capacity tokens and traded through blockchain technology.This allows market participants to understand how they are affected by market rules.Prices and aggregate quantities are public as are the rules that determine the mapping of preferences into unique prices and quantities.The market operator monitors participants' positions-their current product holdings.Forward position transparency helps market operators establish optimized collateral requirements and assess market power.
Simplicity.With transparency comes simplicity.By seeing how the market works and having an opportunity to enhance its effectiveness through participation in governance, market participants will clearly understand the market mechanism.Participation is simplified with powerful bid expression and market tools that translate preferences into an effective strategy.Together, these objectives promote affordability, innovation, and competition in global communications.

Benefits of the open-access approach
• The open-access market provides nondiscriminatory access to fungible units of network capacity, allowing supply to respond to demand requirements that vary with location and time.• Homogenous units of network capacity allow market participants to repurpose efficiently those products to specified heterogeneous needs, allowing for technology-neutral innovation and more competition in communications markets globally.• The pricing mechanism is transparent and efficient, precisely pricing scarce capacity to balance supply with demand at each time and location.This pricing maximizes the use and value of the network and helps communications providers plan their investments and innovations.It also helps them adjust their plans as their needs evolve with changes in consumer demand.• The real-time and forward markets allow for granularity in time and location.Granularity encourages a responsive supply of network capacity when and where it is needed most.• The flow trading approach enables market participants to express preferences and trade in a way consistent with their interests.The method lets market participants satisfy their demands efficiently, create value, and avoid adverse price movements.• The playing field is level and transparent, with buyers and sellers of capacity having complete visibility into the record of trades.
• Transparency of positions enables all market participants to understand and manage the market's effectiveness and to influence improvements through a novel democratized governance structure.• Position transparency also allows the market operator to optimize collateral in the forward market to reduce counterparty risk and reduce participants' costs of satisfying collateral requirements.

Market participants
Network supplier.The network supplier builds, maintains, and operates the network.The network supplier provides the wholesale service capacity, including its quality, security, and resilience.The network supplier facilitates the open-access wholesale market and supports developing and enhancing the open-access market.
Sellers.As the builder and operator of the wholesale service, the network supplier is the principal seller of capacity on the network.Wholesale customers and other market participants who purchase capacity can, in turn, sell capacity back to the market and thereby become suppliers.By bringing together willing sellers and buyers through a clearing house governed by real-time pricing, the network capacity can be utilized more completely by those who value capacity the most at each time and place.
Buyers.Those seeking access to the network capacity include governments, enterprises, and communications providers, including facilities-based wireless and wireline providers, mobile virtual network operators, and other resellers.Technology companies can leverage global connectivity to create innovative products and solutions.
Independent market operator.The market operator is an independent administrator with a simple mission: "We serve our customers by ensuring secure and reliable communications, efficiently priced in an open-access market."In economic terms, the market operator addresses potential market failures, including incomplete markets, incomplete information, market power, entry barriers, and systemic risk.It also conducts transparent and efficient markets by pricing communications services to maximize as-bid social welfare subject to network constraints.As discussed below, buyers and sellers are eligible to become involved in the governance of the independent market operator (and the open-access market itself) through the rights represented by the blockchain.
Decentralized autonomous organization.The market operator board's oversight of the market is supported by the decentralized autonomous organization, which administers blockchain technology.This governance allows consumers, suppliers, and developers to collaborate and make efficient decisions about the direction and future of the market, which eliminates some of the inefficiency that could plague the independent system operator, as exemplified in electricity markets.The decentralized autonomous organization is run by rules encoded through smart contracts, with all transactions and decision-making processes recorded on the blockchain, thereby enhancing transparency.The decentralized autonomous organization is automated, which improves efficiency and saves costs.
Independent market monitor.An independent panel of experts, which reports to the market operator board, is engaged in objectively evaluating and suggesting continuous improvements to the market operator and its board to enhance the performance of the openaccess market.

Governance
A critical complement to the market's open-access nature is its democratic governance.Market participants (buyers and sellers) can acquire, hold, and trade governance tokens representing voting and economic rights.These rights include an ownership stake in the market, a right to receive a portion of the market's revenues, the right to elect representatives to the market operator's governing body, and the right to vote on fundamental matters, such as transaction fees, revenue sharing, and treasury allocation.In this way, market participants can influence the design and operation of the market.The governing body of the market operator is the market operator board (Cramton & Doyle, 2017).

The role of forward trading
Market participants often wish to procure communications needs in advance to manage risk.The forward market enables them to P. Cramton et al. do so.By buying ahead, the participant can lock in favorable terms.Future purchases also let the participant buy gradually, which reduces trading costs, avoids adverse price movements (Black, 1971;Kyle, 1985;Vayanos, 1999), and ensures that final purchases correspond to needs; uncertainty about these needs is resolved over time.
Forward trade provides information about market fundamentals.This granular price information provides the information and risk-management tools essential to innovation.For the network supplier, the price information is critical for optimizing enhancements to the network, such as capacity additions.Finally, prices encourage resiliency by motivating the participants and market operator to take actions consistent with welfare maximization (Cramton et al., 2024).Forward trade creates a virtuous improvement cycle, as shown in Fig. 3.

Distinguishing the physical (real-time) and financial (forward) markets
The market includes a physical real-time market and a financial forward market.Participants use a physical product in real-time by engaging in measured communications through the network.The communications are priced in real-time to balance supply and demand subject to network constraints.The 1-h real-time window means that imbalances typically are insignificant.If real-time rationing is necessary, rationing is limited to throttling or delayed delivery of the regular service type as shown in Fig. 4.
Forward products derived from real-time capacity products are financial; deviations between forward and real-time positions are settled financially.Efficient settlement rests on robust pricing and the elimination of counterparty risk.The market operator manages counterparty risk with collateral obligations that depend on deviations between the participant's forward positions and anticipated needs.The use of smart contracts settled on the blockchain further reduces settlement risk.

How will the market work?
All aspects of participation in the open-access market are voluntary, including buying and selling capacity through capacity tokens and acquiring and exercising governance rights through governance tokens.Participants can purchase capacity in the financial forward market and the real-time physical market as price-takers without the need to schedule consumption in advance.

Products
The primary products traded are the capacity tokens representing capacity on the network, measured in gigabytes, and the governance tokens.These are best thought of as systemwide capacity and governance tokens.The systemwide capacity token is then broken down into communications in gigabytes in an hour, region, and communication type through the open-access auction platform.There are three types-premium, regular, and fast.The communication types differ in their real-time routing optimization.Premium is optimized for reliability and speed; it is nearly never rationed.Regular is optimized for reliability and speed but is rationed as necessary based on network conditions.The premium/regular distinction allows critical communications to be prioritized in the event of excess real-time demand (Chao et al., 1986).Fast is optimized solely for speed, not reliability.Fast is a specialty product tailored to the exacting needs of high-frequency traders and others sending messages where every millisecond matters.There are more geographic aggregations as population density and economic activity decline.To simplify, the globe is partitioned into a manageable number of regions.There is little point in differentiating between, say, two locations in the Pacific 100 km from any land mass.In contrast, there are meaningful demand differences between, say, New York City and Atlanta.New York City and Atlanta should be in separate partitions whenever there is economic justification for differential pricing between the two cities.A partition with about five hundred regions seems a good starting point.As the market matures, finer geographic granularity may be desirable.
Regardless of the partition, it is helpful to visualize a hierarchy of partitions of increasing granularity.At the top of the hierarchy is the entire globe.
With 500 regions, there would be 24 × 500 × 3 = 36,000 real-time products each day (hours per day × # of regions × # of product types).The hourly time granularity for global communications is preferred.Less granular options, such as peak and off-peak, are problematic since these designations are location-dependent.The hourly product has little extra user or system cost.Indeed, finer time granularity is anticipated as the market matures.

Trading methodology
Flow trading (Budish et al., 2023) allows market participants to adjust user-defined portfolio positions efficiently as information changes over time.Despite fine product granularity, liquidity is not compromised since demand is cleared simultaneously by product independent of portfolio, and trade occurs gradually.Auctions occur every hour for all products.The bidding window starts when prices from the preceding hour are posted, a few minutes after the hour, and lasts until the hour's end.During the bidding window, market participants may adjust their orders.The orders at the end of the bidding window (on the hour) are final.Each order is a piecewise-linear decreasing demand curve, represented by two or more quantity-price pairs.The order also specifies the linear combination of products for which the demand curve applies.The price is in $/GB.Thus, quantity represents the rate of trade-the quantity in gigabytes that trades over the unit of time at a particular location.Market participants either upload their orders or enter them directly into the auction platform.Changes to orders are allowed until the bidding window closes on the hour.Orders that are not valid are rejected.On the hour, the auction platform processes the final orders and determines the prices and quantities that maximize as-bid social welfare.
Note that in a blockchain implementation, the currency is capacity tokens.The token can be exchanged for any other crypto or fiat currency on exchanges outside the open-access market.
Mathematically, the form of preference expression guarantees unique quantities (Budish et al., 2023, Theorem 1).Prices exist but may not be unique (Budish et al., 2023, Theorem 2).However, unique clearing prices result with an intuitive tie-breaking rule: If a product has multiple clearing prices, the price closest to the preceding clearing price is selected.The auction platform revises each participant's position based on the quantities implied by the prices.Each participant can view and download prices and the revised position anytime during the bidding window.This process repeats every hour.Orders persist until changed or canceled.Thus, if the user wants to maintain the same preferences because nothing has changed, then the user does nothing.The same orders will continue to be processed every hour until the user submits a change.The 1-h clearing frequency is a parameter of the market.Faster frequencies, every minute or second, are possible.

Settlement and collateral
Every hour, the auction platform updates the settlement for each participant.If the user's excess collateral falls below a warning trigger, the user is warned.If the user's excess collateral falls below zero, future trades that would increase the participant's collateral requirement are not allowed.For every order, the portion that would shift the user to a less balanced position are cancelled.
Collateral requirements are based on a to-be-developed optimization.This approach will maximize market stability while minimizing unnecessary capital commitments from participants.The key inputs in determining collateral are the participant's current position and the participant's expected position.The participant estimates the latter and reports it to the market operator.Excessive deviations between reported estimates and realized positions increase the participant's collateral requirements.
Once per week, or more frequently if desired, the accumulated settlement over the preceding 7 × 24 h is reported to each market participant.Consistent with the weekly accumulation, an automatic transfer to or from the participant's capacity token account is made.If the transfer fails, then the participant has 24 h to resolve the issue.After 24 h, any payment due is taken from the participant's collateral account, and the user is prohibited from further trades that would put the participant in a less balanced position.

Transparency
The auction platform publicly posts prices when the computation is complete, usually within a few minutes of the end of the hour.Each participant also learns its revised position.The platform lets participants view and download prices, a participant's current position, and the most recent trade rates.

Market operator
The market operator oversees the real-time and forward market functions through the blockchain to ensure smooth operation.The market operator provides monthly, quarterly, and annual reports on the market performance to the market operator board.Participants have direct access to the blockchain technology from which those reports are generated.The market monitor also studies and discusses the market's performance in state-of-the-market reports.

Product granularity
Flow trading allows finer product granularity.The reason is that participants place persistent portfolio orders that induce a smooth trade flow among all products.First, look at the forward prices to understand how this would work.Figs.5-7 show the yearly, monthly, and hourly hypothetical forward prices for the New York premium capacity during a weekday. 6here are many prices, but they are readily understood by the eye and analyzed with computer modeling.The example above illustrates time-of-day and day-of-week price impacts and greater volatility of prices, the closer to real-time.Prices are updated hourly when the market clears.
Participants trade forward products up to five years ahead and adjust positions by hour.
A simple and effective flow trading strategy is trade-to-target, illustrated in Fig. 8. Participants state their target and the rate at which they want to move toward the target.For example, a service provider might set its target to its capacity needs, increasing linearly from zero to expected demand, moving from 5 years ahead to real-time.With flow trading, the participant specifies the rate at which it desires to make this adjustment as a function of price.A participant wants to buy more quickly when the price is low and sell more quickly when the price is high.This is expressed as a linear net demand curve for each product.The participant's urgency to trade also depends on the adjustment size and the closeness to real-time.Trading faster is preferred when larger adjustments are needed closer to real-time (Cramton et al., 2024).

Efficient trading
We envision five years of annual forwards (by hour, weekday-weekend), 12 months of monthly forwards (by hour and weekdayweekend), and 30 days of hourly forwards for each region and product type (premium, regular, and fast).This implies (3 product types) × (24 h/day) × [(2 day types) × (5 years +12 months) + 30] = 4608 products per region.With five hundred regions, this is 2.3 million products.We can summarize the key features of the bidding language in two theorems from Budish et al. (2023) and an immediate corollary.The mathematics below borrows freely from Budish et al. (2023).
Let V i (x i ) denote the dollar utility of order i from a trade rate of x i = D i (p i ) in portfolio units per hour, where flow portfolio demand D i (p i ) is given by equation (1): To find V i (x i ), we first define the marginal utility function M i (x i ) as the inverse demand curve, p i = M i (x i ).The inverse demand  curve maps order i's trade rate . 7 Rearranging equation (1), we have: The value of M i (x i ) measures marginal as-bid flow value in dollars per portfolio unit.Utility V i (x i ), as a function of the trade rate x i , is defined as the integral of the marginal utility function over the interval [0, x i ]: (3) Since the marginal value is linear in x i , the total value is quadratic and strictly concave in x i : We assume V i (x i ) as defined for all x i ∈ R, with order specifications imposing the constraint x i ∈ [0, q i ].
Our problem of finding market-clearing prices is formulated as two optimization problems: a primal problem of finding quantities that maximize as-bid dollar value and a dual problem of finding prices that minimize the cost of non-clearing prices.The first-order conditions for the optimality of these two problems imply market-clearing prices and quantities.
The market operator, acting analogously to a social planner, chooses a vector of trade rates for all orders x = (x 1 , …, x I ) to maximize aggregate value, defined as the sum of pseudo-utility functions across orders, subject to market-clearing constraints and trade-rate constraints: The objective function V(x) is concave because it is a sum of concave functions.Indeed, this is a quadratic program since the objective function is quadratic and the constraints are linear.To make this quadratic structure apparent using matrix and vector notation, let W denote the N × I matrix whose i th column is w i .Let p H denote the column vector whose i th element is p H i .Let D denote the I × I positive definite diagonal matrix whose i th diagonal element is / q i .Then, the problem in equation ( 6) may be written compactly as We first show that quantities that maximize aggregate utility exist.Then, we show that market-clearing prices exist by examining the dual problem of the utility maximization problem.We then show that there is a unique mapping of orders into prices and quantities.Uniqueness of prices and quantities is important for transparency.These are standard results of convex optimization (Bertsekas, 2009), derived from strict convexity and continuity.Our presentation follows Budish et al. (2023).
Theorem 1. Existence and Uniqueness of Optimal Quantities.A unique vector of trade rates x exists, which solves the maximization problem in equation ( 7).
To prove that market-clearing prices exist, we exploit the duality between the problems of finding optimal prices and quantities.For this, we define a Lagrangian function of the vector of trade rates x with three constraints: (1) the market clears (Wx = 0); (2) the trade rates are greater than or equal to zero (x ≥ 0); (3) the trade rates are less than or equal to their maxima (x ≤ q).In vector notation, the Lagrangian is defined by Since the multipliers associated with the market-clearing equality constraints have the economic interpretation of market prices for assets, we use the notation π = (π 1 , …, π N ) ⊤ for these multipliers.Two vectors of multipliers, μ = (u 1 , …, μ I ) ⊤ and λ = (λ 1 , …, λ I ) ⊤ , are associated with inequality constraints on trade rates.
The dual problem associated with the primal problem of maximizing aggregate utility in equation ( 7) is then defined by 7 For trade rates in the interval (0, q i ), the fact that the order chooses an interior trade rate tells us that the order's as-bid marginal utility is equal to the corresponding price in the interval . The same logic extends to the boundary points 0 and q i , corresponding respectively to prices p H i and p L i , by assuming as-bid utility is continuous.
The dual problem is a minimization problem with infimum g defined by (10) The dual problem in equation ( 10) is formulated as an infimum rather than a minimum because we have not yet shown that there exists a solution (π, λ, μ) that attains the infimum.
Theorem 2. Existence of market-clearing.There exists at least one optimal solution (π, λ, μ) to the dual problem in equation ( 10).The solutions x and (π, λ, μ) are a primal-dual pair which satisfies the strict duality relationship Theorem 2 does not guarantee that market-clearing prices are unique.The set of market-clearing prices is convex and may be unbounded.A trivial example occurs when all orders are buy orders for individual assets, and there are no sell orders.Then, any sufficiently high price clears the market with zero trade.There may also be cases where the market-clearing price is not unique even when trade occurs.A trivial example occurs when there is one buy order and one sell order for the same asset (or portfolio) with the same maximum rate, and the buyer's lower limit price exceeds the absolute value of the seller's lower limit price.In this case, there is an interval of prices where both orders are fully executable.However, a natural tie-breaking rule makes the prices unique.
Closest-to-prior-prices rule.If more than one price vector supports the optimal quantity vector, select the price vector closest to the prior price vector.

Corollary 1. Uniqueness of quantities and prices. Prices and quantities are unique with the closest-to-prior-prices rule.
Proof.The set of prices that support the unique optimal quantities is convex.The closest point in a convex set to a point is unique.End proof.
The closest-to-prior-prices tie-breaking rule is especially appropriate in our frequent batch auction setting, in which prices evolve slowly from the gradual trade of persistent orders.
These unique prices and quantities can be found quickly.Flow trading involves the solution of the following optimization program: where D is a non-negative, diagonal matrix.To exploit the near-separability of the problem, we employ the alternating direction method of multipliers (ADMM) (Boyd et al., 2011).This technique solves an optimization problem of the form min We define an indicator function C(b) = 0 if b is true and ∞ otherwise, i.e., C(a ≤ x ≤ b) and C(Wx = 0) will be used to enforce our problem constraints.We choose where ⊗ denotes the Kronecker product.This splits the minimization across two sets of variables: x, which correspond to rates of execution of each order, and z = (z 1 , z 2 , …), which are the trade rates each fulfilled order imposes across the space of products, i.e. (We i )x i = z i for each order i.ADMM proceeds by formulating the augmented Lagrangian, then repeatedly minimizing it via a Gauss-Seidel pass on the primal variables (x,z), followed by a dual ascent on y.When substituted into the ADMM framework, the splitting scheme yields a compelling algorithm.First, it is straightforward to show that the dual variable y = 1 ⊗ π, where π are the shadow prices.Second, the two subproblems needing to be solved as part of the Gauss-Seidel pass are trivial.
The first subproblem, necessary for the x-update, takes the form min for some r that varies per iteration.Being fully separable, we can write the solution explicitly: P. Cramton et al.The second subproblem, necessary for the z-update, takes the form min where the {c k } vary per iteration.This can be solved analytically using elementary calculus and evaluated by simply averaging the {c k }.
Both subproblems efficiently scale to arbitrarily large problem sizes and are easily parallelized on a CPU or GPU.Research is ongoing to fine-tune the implementation's penalty and over-relaxation parameters.
We have built a prototype platform to implement forward markets in many domains, such as energy, communications, and transportation.The basic architecture is depicted in Fig. 9.The core infrastructure is a forward market system and a low-level flow trading system that performs optimization.
Details of flow trading are shown in Fig. 10.It consists of an application programming interface, a database, and an optimization engine.
Although it may be hard to imagine trading so many products, the flow trading technology makes this easy by exploiting the power of convex optimization.From a computational complexity viewpoint or a user experience viewpoint, there is little difference between a hundred, a thousand, or a million products.Bid entry and optimization are readily managed with information technology.Budish et al. (2023) demonstrate how computation times vary with the number of orders and assets (products); see Fig. 11.The computation to find unique prices and quantities can be done on a single server in about one hundred seconds, allowing clearing every hour.The Appendix includes sample code for a simple flow trading implementation.

Simplified participation in a complex market
Thanks to a simple and effective method of preference expression, participation is straightforward, even though the market is solving for a complex set of dynamic demand and supply variables.A participant's strategy depends on three essential inputs: risk attitude, capital cost, and expected hourly net demand.
Standard financial modeling provides the simplest way to represent risk attitude and capital cost.Two scalar parameters can define the participant's utility function.Capital cost is the participant's discount rate or time value of money.Risk attitude determines the concavity of the utility function.Assuming constant absolute risk aversion, a risk-neutral participant would have a risk parameter of zero, implying linear utility.Risk-averse participants have a risk parameter greater than zero.Larger risk parameters indicate greater risk aversion.
The final input is the participant's hourly expected net demand.This is easy for a pure financial participant; net demand is zero for all hours.For others, it is a complex technical calculation that requires good knowledge of customers for buyers and portfolio for sellers.Hybrid participants who own a portfolio of capacity tokens and serve consumers must estimate their anticipated supply and demand.However, participants in any communications wholesale market need to estimate net demand to decide how to participate.This difficult input is necessary regardless of the market's design (Cramton et al., 2024).
A trading tool is developed to help market participants understand how the forward market works and how to participate easily.The core of the tool is straightforward.The user specifies the risk attitude and capital cost parameters.The user then uploads her expected net demand as a.csv file.For an arbitrageur, this is a matrix of zeros; no upload is needed in this case since the zero matrix is Fig. 9. Forward market architecture.
P. Cramton et al. the default.The arbitrageur's target position is zero for all products.For a buyer and seller (or hybrid), the trader's expected net demand (demand minus supply) defines the target position in each hour.The target is the participant's expected net demand in each hour multiplied by the trader's target percentage.The target percentage increases linearly from 0 percent to 100 percent from five years ahead until real-time.
As time passes, uncertainty resolves, and the participant adjusts its target strategy.The adjustments are modest.This is a simulation of a participant of moderate size (about 240 GB/h in each region).
Fig. 12 shows how the target can be reached with a flow trade rate, assuming a flow trade rate as (communications adjustment)/(8 × days ahead).Flow trade rates are small if the days ahead are large.There are many hours to trade when we are far from real-time.This is why the flow trade rates are so small many days from real-time.Even close to real-time, the required flows are only a handful of gigabytes, which is small for a 240 GB/h service provider.The quantity traded is never zero but always small, reducing risk and adverse price impact.
The output lets the user visualize outcomes and how outcomes vary with variations in specified risk attitude and capital cost.It also helps users determine the incremental gain or loss from adding customers (increasing demand).This incremental calculation is essential in pricing and investment decisions.

Liquidity
Traditional markets manage liquidity by limiting the number of products.For example, wheat trading involves many grades and classifications, which vary by country and the organization responsible for grading.The United States Department of Agriculture categorizes wheat into eight classes based on kernel hardness, color, and planting season.Within these classes, wheat is further graded on a scale from 1 through 5 based on additional attributes like test weight, defects, and moisture content.There are forty wheat products traded in the US.
As explained above, modern markets like the open-access market can trade products with much richer granularity.Liquidity is managed by allowing near-perfect substitution among products that are near-perfect substitutes.Through gradual adjustment of portfolios, the global capacity tokens become fungible network capacity for communications at particular times and locations.
The forward market has high transparency, robust pricing, and low transaction costs, which favors liquidity.The forward market has three further advantages.First, preferences are convex.Market participants enter piecewise linear net demand curves, which yield a quadratic objective in the clearing optimization.Second, because the forward market is conducted well before the real-time market, the market participants have time to adjust positions as uncertainty resolves.Third, the frequent batch auction approach allows participants to make thousands of minor adjustments over months and years.Slow trading enables participants to minimize adverse price movements, improving the market's competitiveness and increasing liquidity.

Counterparty risk
Efficient and transparent forward trade reduces counterparty risk and lowers costs.Vibrant forward trade puts market participants in more balanced positions, reducing risk and market power and thereby reducing system cost.
Electricity markets provide a vivid example of the benefit of balanced positions in reducing counterparty risk.Consider the costly defaults in electricity markets over the last twenty years.In the 2000-2001 California electricity crisis, the utilities entered a long scarcity period caused by drought (low hydro production) with a large short position (Borenstein, 2002).The utilities required rescue by the state, costing about $40 billion (California State Auditor, 2001).In the February 2021 Texas crisis, the market participants were in more balanced positions, and defaults were rare despite a real-time value of electricity of over $50 billion in four days (Cramton, 2022).In Britain's crisis of 2021-2022, poorly hedged suppliers defaulted, costing consumers more than $10 billion (Waddams, 2023).
In the forward market, imbalanced positions are known, and the associated risk is priced and mitigated through higher collateral.Overall system risk is reduced.

Open access motivates flexibility
Efficient prices reward those providing flexibility.Market participants can easily see and enjoy the value of flexibility.Transparent and efficient prices will motivate demand-side innovation essential to consumer engagement (Cramton et al., 2024).

Open access is pro-competitive
A few concentrated firms, static pricing and services, and a need for more innovation and competition are hallmarks of today's communications markets.With an open, nondiscriminatory wholesale market, enhanced through granular real-time and forward market pricing mechanisms that consider time and place, more fungible network capacity is made available at more affordable prices.This will improve the ability of smaller and more innovative communications operators to be competitive in their respective markets.As noted above, it will also encourage operators to be more flexible with their capacity portfolios, prompting them to sell excess capacity when it is not needed rather than strand it behind a walled garden.

Summary and conclusions
This paper develops an open-access market to manage network congestion and optimize a network's use and value, building on recent advances in wholesale electricity markets (Cramton et al., 2024).The wholesale market includes real-time and forward markets.The initial conceptual application is intersatellite communication networks-optical (laser-beamed) mesh networks in space.
This physical real-time market with priority pricing ensures a balance between offered supply and bid demand at each time and location.The product, represented by a crypto token, is gigabytes of three communication types-premium, regular, and fast-in a 1-h time window at a location, say, New York City, 9-10am on August 14, 2026.The scarce capacity is used by those who value it the most at a price that balances supply and demand.The real-time market is the foundation for the financial forward market.The forward market enables market participants to take capacity positions in advance of real-time, consistent with their anticipated real-time needs.Participants manage risk and profit through gradual trade as uncertainties resolve.Participants can efficiently convert global communication rights into their realized communication needs at each time and place.An independent market operator conducts a transparent market.
The open-access market operates without friction using flow trading (Budish et al., 2023).Participants bid persistent piecewise-linear downward-sloping net demand curves for portfolios of products.The market operator clears the market every hour, finding unique prices and quantities that maximize as-bid social welfare.Prices, aggregate quantities, and the slope of the aggregate net demand are made public through a blockchain platform.The market operator observes positions, enabling it to optimize collateral requirements to minimize default risk.
Participants employ trade-to-target strategies with only a handful of portfolio orders, enabling the efficient trade of millions of interrelated time-and-location-specific products.In each hour, the participant has a current position-the quantity held of each product-and a target position-the desired portfolio.The trade-to-target strategy specifies the rate at which the participant moves from its current position toward its target.To best manage risk and avoid adverse price impact, participants trade gradually, updating their target as circumstances change.Participants' strategies depend on their communication needs, risk tolerance, capital cost, and market fundamentals.Fundamentals are richly conveyed in the market operator's hourly clearing reports.The market operator provides tools for participants to translate their preferences into an effective strategy.Despite the complexity of the market, participation is easy.
Market participants also have an opportunity to take ownership and governance roles in the market by acquiring and trading governance tokens, which are also bought and sold through the market's blockchain platform.These tokens represent a bundle of rights akin to rights attached to shares held by shareholders in a private or public company.Holders of governance tokens are eligible to receive allocations of market revenues and to vote in elections for representatives to the market's governing body.
The ideas presented here are familiar.The most important points have been well-understood for decades if not centuries.The inefficiencies created by imbalanced ownership appear in Myerson and Satterthwaite (1981), Cramton et al. (1987), andAusubel et al. (2014) and are empirically documented in many studies (Borenstein, 2002;Wolak, 2003;Wolfram, 1999).Vickrey (1961) pricing can mitigate market power but only with non-anonymous, discriminatory prices that seem unfair to many and are anticompetitive in favoring larger parties.More frequent trade provides a better means to mitigate market power (Black, 1971;Coase, 1972;Kyle, 1985;Vayanos, 1999), especially when dynamic trade is natural to manage risk as circumstances change.The form of trade matters.Frequent batch auctions can eliminate an arms race for speed (Budish et al., 2015) and have been implemented in electricity markets (Cramton & Ockenfels, 2024), especially when combined with flow trading (Budish et al., 2023), which brings an effective language of preference expression.Participants can adopt simple trade-to-target strategies, allowing flexible risk management and providing efficient and transparent price signals.These prices summarize the essential information for efficient investment (Cramton et al., 2024).
The ideas apply to any commodity, especially those with time and location elements.In this paper, we have elaborated on trade in optical mesh networks in orbit for intersatellite communications.Considering other markets, the most obvious is mobile communications.Price is a more efficient instrument for managing congestion than rationing with dropped calls or throttling (Cramton & Doyle, 2017).
Infrequent spectrum auctions are used to assign mobile communications spectrum today.These auctions could be replaced by a much more flexible assignment of spectrum in time and place.We need communication technologies that are sufficiently flexible.Then, spectrum can be a commodity traded in real time to balance supply and demand, supported by a forward spectrum market.Doing so would address the market power and competition issues of today's oligopoly model.Rather than continued consolidation, mobile communications could shift to an open-access model of vibrant competition like the internet enabling Eli Noam's vision for open access in spectrum-based communications markets (Noam, 1998).Communications is the natural product, since that is the commodity buyers consume.However, as devices become more flexible, it may be possible to commoditize spectrum over short time intervals.Then, there could be multiple commodities: real-time markets for communications and spectrum, with spectrum serving as an input market for the communications end product.
Various organizational structures are possible for the communications and spectrum markets.The communications market could be conducted by a neutral operator organized by one or more network owners.The spectrum market, as an essential input of communications, could be conducted by a similar neutral market operator; however, the spectrum market would be more tightly regulated by the communications regulator.Wholesale electricity markets provide an example.The electricity regulator designates an independent system operator to conduct the open access electricity market to provide reliable electricity at least cost.This structure has worked well in restructured electricity markets (Cramton, 2017).Natural gas is an input to electricity production, while spectrum is an input to communications.In the future, real-time and forward spectrum markets may replace today's spectrum auctions, fulfilling Noam's (1998) vision that spectrum auctions are tomorrow's anachronism.
We An open-access market for global communications offers an early entry into the brave new world of efficient pricing of essential commodities.Transparent and efficient pricing benefits market participants by maximizing the value of the scarce communications capacity.The prices also provide crucial information for efficient investment and operation of network resources.Do you need to worry about a short squeeze as in other forward commodity markets?

CRediT authorship contribution statement
The forward market settles against the real-time price.All forward products are financial derivatives of the physical real-time products.
However, as in any forward market, a short squeeze is possible.The squeeze would take place in the real-time market.A participant takes a significant imbalanced position in the forward market, causing others to take imbalanced forward positions and then squeeze them in real-time.A dominant supplier has a comparative advantage in executing the squeeze.A supplier buys a large quantity forward, leaving others short, then offers supply at high prices in real-time and strategically withholds in real-time.During periods of scarcity, enhanced market power improves the effectiveness of such strategies.
The forward market mitigates this possibility through transparency of positions.The market operator and market monitor would observe the imbalanced position, prompting action.Moreover, the single-price auction makes a squeeze prohibitively expensive.
Recall Salomon Brothers' famous squeeze in the US Treasury markets in 1990-1991.To be successful, Salomon Brothers needed to hold a considerable position.They acquired majority shares in some Treasury auctions.Although illegal, winning a majority was possible because of the pay-as-bid pricing and large price-tick size at the time.Salomon Brothers could acquire most of the issue and squeeze the short dealers in the subsequent market by bidding at one tick above the obvious clearing price.Acquiring such a significant stake would be prohibitively expensive with single pricing, which we have here.
Hundreds of market participants exist in the forward communications market.The participants include natural buyers, natural sellers, and arbitragers.Natural buyers and sellers also function as arbitragers-the arbitrage behavior results in price convergence.In electricity markets, the forward price equals the expected real-time price plus a small risk premium of less than two percent (Jha & Wolak, 2023).
The market is highly competitive.Therefore, the scope for strategic bidding is limited.Flow trading further mitigates incentives for strategic bidding by incentivizing participants to seek balanced positions to manage risk and limit collateral.With balanced positions, there is no incentive to distort bids.
Market power only arises close to real-time.Then, market participants can take actions that may result in more significant and favorable price impacts because other participants will not have time to take corrective measures to mitigate this behavior.

Example of preference expression and market clearing
To fix ideas, consider three market participants (Ann, David, and Sally), two locations (New York and Tokyo), and two times (today and tomorrow).Our participants submit bids in today's forward market to hedge tomorrow's prices.Deviations from today's position will be realized tomorrow and settled at tomorrow's prices.
Ann is an arbitrageur.She participates in the market to exploit her expert understanding of prices.Her strategy is classic: buy low and sell high; do not drift far from a zero position.
Sally is a US-based communications service provider with a portfolio of capacity tokens that she sometimes deploys for domestic communications operations.Her portfolio exceeds her needs and often sells capacity into the open-access market.Sally pursues a trade-to-target strategy designed to maximize profit and limit risk.
David is a wireless reseller.He has a portfolio of consumers he is obligated to serve but never wants to hold excess capacity.He participates in the market to maximize profit and limit risk.
Although Sally is a seller and David is a demander, both recognize that it is helpful, like Ann, to participate in buying and selling depending on prices and other circumstances.Thus, all market participants express net demand curves that involve selling or buying depending on price.Participants express quantity as a flow, the rate of trade over a 1-h window (GB/hour).
First, suppose there is a single forward product, tomorrow's premium capacity.Each demand curve is expressed as a vector of quantity-price pairs, as in Table A1. Figure A1 shows the net demand curve for each participant.Ann expects tomorrow's premium demand to be about $6/GB.She wants to buy when the forward price is less than $6 and sell when it is higher than $6.To protect herself from going too long or short, Ann bids a net demand curve that becomes steeper when the absolute value of the quantity is larger.This shape is a risk management element in all three curves: convex for negative amounts (buying) and concave for positive quantities (selling).It also mitigates adverse selection and moral hazard.For example, Sally may know that she will take some of her spare capacity offline during the premium period, creating an unexpected price rise in real-time.Ann protects herself from such events by requiring a larger price discount to accept a larger forward position.
Sally also expects tomorrow's premium price to be about $6/GB.However, as a natural seller, Sally is willing to sell at prices a few dollars below $6.Sally is happy to sell ahead an even larger portion of her expected production at higher prices.At prices well below $6, Sally is glad to buy ahead, knowing that the opportunity to sell tomorrow should reap profits.In the forward market, her offer must reflect the opportunity cost of selling the production tomorrow, which is about $6/GB.For Sally, like Ann, the forward market is about arbitrage and risk management.Her offers reflect opportunity cost, not marginal cost.
David anticipates that tomorrow's premium price will be about $6/GB.However, he is obligated to purchase his capacity needs tomorrow.He recognizes the possibility of demand shocks that could send the premium price to high levels.Thus, he adds a significant risk premium to his bids.He wants to buy a large share of his capacity needs unless the forward price is high.This preference is why David's net demand curve is significantly above Ann's and Sally's curves.His curve is similar in other respects: convex for negative quantities and concave for positive amounts.
All the curves are required to be piecewise-linear and decreasing.This language gives market participants enormous flexibility in expressing demand.The participant can approximate any continuous, decreasing demand.In this application, assuming that a participant's true preferences take this form is natural.An essential advantage of this form is that it implies unique prices and quantities, except in unlikely instances of no trade.
To find the clearing price, we add the individual demands in the quantity dimension, which yields the aggregate demand curve in Figure A2, focusing on the aggregate demand segment that includes the clearing price.The clearing price is where aggregate net demand is zero, a price of $6.11.The price is unique because the aggregate demand is continuous and strictly decreasing.Now, consider two products: regular and premium.Regular is for buyers who accept the slight possibility that their throughput will be rationed; premium is for buyers who find rationing unacceptable except in rare circumstances.How do the bid expression and market clearing generalize?With two products, our participants can bid on one or both products individually or on any linear combination of the two products.
Ann bids on two products individually, and Sally and David bid on a linear combination of premium and regular, consistent with their objectives.Again, each order is a vector of quantity-price pairs, as shown inTable A2.  Figure A4 shows the resulting demand curves.Each order is a piecewise linear decreasing curve.The participants can submit as many orders as they want, for individual products or any linear combination of products.Ann's regular order is her premium order shifted down by $3.She expects regular to clear at about $3.She wants to buy premium and regular communications at prices below $6 and $3 and sell them at higher prices.
David bids for a 60-40 split of premium and regular.His expected regular demand is 80 percent of his premium demand.Thus, the 60-40 split is consistent with his anticipated demand.He buys more premium communications because he appreciates its better throughput.He knows he will have to pay a risk premium for premium communications, but he is happy to do so to improve his communications.
Sally bids for a 50-50 split of premium and regular communications, slightly less than the 55-45 split she desires in real-time.She offers less premium communications because of the greater risk it entails.She knows shortages are possible, and the stringent premium quality is more challenging to satisfy.She expects a higher price on the premium communications she sells ahead.The products clear product-by-product.The number of prices is equal to the number of products.Market clearing involves finding two prices, premium and regular communications, that simultaneously balance supply and demand given the collection of orders.The clearing prices of $6.23 and $2.91 for premium and regular communications are displayed in Figure A5.These prices imply Ann sells 0.61 of premium communications and buys 0.16 regular.Sally sells 1.69 each of premium and regular communications.David buys 2.29 premium and 1.58 regular.
This example illustrates the beauty of the flow trading approach.The participants have enormous flexibility in expressing preferences.Then, given a collection of piecewise linear, decreasing demand curves, the market operator finds unique market clearing prices and quantities by solving a linear system.Larger problems with more products and more participants are solved similarly.The linear system to be solved is larger, but the computational needs are similar.Indeed, as discussed later, computation times tend to increase linearly with the number of products and orders.

Fig. 2 .
Fig. 2. Population density by country, people per sq km, Our World in Data, 2022.

Fig. 3 .
Fig. 3.The virtuous cycle of improvement stemming from forward trade.

Fig. 4 .
Fig. 4. Regular service may be throttled or delayed when demand exceeds supply in real-time.

Fig. 8 .
Fig. 8.A participant's inputs imply a trade-to-target strategy and resulting outputs.

Fig. 11 .
Fig. 11.Computation time for challenging cases by number of orders and assets (products) (Budish et al., 2023); (the slight discontinuity in the right panel has to do with the cache size of the CPU).
have stressed the benefits of open access.But what about the costs?Perhaps the costs may dominate the significant benefits.The answer is that historically, serious costs stood in the way of open access.Information technology advances have eliminated these costs.The open access benefits can be enjoyed today without cost.

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Fig. A2 .
Fig. A2.Aggregate net demand curve around the clearing price for tomorrow's premium.Finally, we determine the quantities by evaluating everyone's net demand at the clearing price, as shown in Figure A3.David buys at a rate of 3.8 gigabytes/hour; Sally sells at 3.6 gigabytes/hour; Ann sells at.3 gigabytes/hour.The net demand is zero, as required by market clearing.

Fig. A3 .
Fig. A3.Clearing quantities for each participant are uniquely determined from the clearing price.

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Fig. A5 .
Fig. A5.Clearing quantities for each participant are uniquely determined from the clearing prices.

Table A1
Piecewise linear net demands (GB/hour) as a function of price ($/GB)

Table A2
Piecewise linear net demands (GB/hour) as a function of price ($/GB)