Multi-item auctions for automatic negotiation

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Abstract

Available resources can often be limited with regard to the number of demands. In this paper we propose an approach for solving this problem, which consists of using the mechanisms of multi-item auctions for allocating the resources to a set of software agents. We consider the resource problem as a market in which there are vendor agents and buyer agents trading on items representing the resources. These agents use multi-item auctions, which are viewed here as a process of automatic negotiation, and implemented as a network of intelligent software agents. In this negotiation, agents exhibit different acquisition capabilities that let them act differently depending on the current context or situation of the market. For example, the ‘richer’ an agent is, the more items it can buy, i.e. the more resources it can acquire. We present a model for this approach based on the English auction, then we discuss experimental evidence of such a model.

Introduction

The steadily increasing interconnection of devices raises many research issues with regards to the ways in which all these distributed machines can interact effectively with other humans or machines. Artificial intelligence and software engineering have a role to play in how the computers can interact in a ‘rational’ way. Several groups of researchers propose autonomous agents for addressing this big issue. Autonomous agents are software systems that are capable to independently act on open, unpredictable environments. They are considered as a new paradigm for developing software applications involving artificial intelligence techniques and distributed computing.

Indeed, agent technology is a significant area of interest for such applications as telecommunications, information management, internet search engines, electronic commerce, computer games, interactive cinema, information retrieval and filtering, user interface design, industrial process control, planning and logistics, etc. The successful adoption of this technology in all these areas will have a profound impact both on industry, and also on the way in which future computer systems will be conceptualized and implemented.

At present, there is much debate about what agent-hood is exactly, and there is nothing approaching a consensus, as it is generally the case for any new field. However, an increasing number of researchers define agents as being:

  • 1.

    situated or embedded in a particular environment;

  • 2.

    designed to fulfil specific roles;

  • 3.

    clearly identifiable entities with well-defined (and limited) resources and interfaces;

  • 4.

    autonomous in the sense that they have control over their behavior;

  • 5.

    capable of exhibiting flexible behavior which can be reactive, proactive, sociable or persistent.

In the context of concurrent and distributed systems, it becomes obvious that a single agent is insufficient. Many applications, if not most of them, require multiple agents, called also multi-agent systems (MAS). In such systems, knowledge, action and control are distributed among the agents, which may cooperate, compete or coexist depending on the context in which they operate. According to Weiss [1], there are two main reasons which drive forces behind the growth of the MAS paradigm in recent years.

The first is that MAS have the capacity to play a key role in current and future computer science and its applications. Modern computing platforms and information environments are distributed, large, open, and heterogenous. Computers are no longer stand-alone systems, but have become closely connected both with each other and their users. The increasing complexity of applications often lead to the design of ‘individual’ software agents instead of a large entity which is in general less flexible. The technology that MAS promises to provide, are among those that are urgently needed for the Internet, telecommunications, TV-web, e-commerce, e-business, etc.

The second reason is that MAS have the capacity to play an important role in developing and analyzing models and theories of interactivity in human societies.

These two reasons combined show the relevance of MAS for understanding, implementing and operating complex socio-technical systems as represented by e-business systems.

In this paper we propose a model for multi-item auctions that has a strong relationship to the efforts in building MAS. We start from the interactivity between humans in a market, especially for the multi-item sell/buy negotiations, and we try to realize it under the form of a negotiation between software agents.

Auctions are a market mechanism already introduced in the ancient world. Traditionally, they allow selling rare and unusual goods, and apply in situations where a more conventional ‘market’, in which buyers consider the price as given, do not exist. A large informal body of knowledge on auctions has been in existence for centuries, and a more formal, game theoretic analysis of auctions began in the 1960s with the pioneering work of Vickery [2]. The field of micro-economics and game theory that studies these and related issues is often called ‘mechanism design’ or ‘implementation theory’. An introduction to this field can be found in the textbooks [3], [4].

With the widespread availability of the internet and e-commerce technologies, economists have started to consider auctions as an important economic model. Indeed, the theory of auctions exhibits many interesting features at the practical, empirical and theoretical level. Paul Klemperer [5] gives three reasons why the theory of auctions is relevant to economists:

  • 1.

    A growing number of large volume transactions are realized through auctions. Examples include the many auctions organized by governments [6], the enterprise wide electronic procurement systems for all sorts of goods, or the electronic auction markets such as EBay [7], [8].

  • 2.

    Auctions offer relatively simple mechanisms in a well-defined economic environment. They offer thus to economists a vast field for experimental research allowing to obtain empirical results that can be suitably validated.

  • 3.

    The theory of auctions has already revealed many scientific results in economy, which have allowed to develop new methods for pricing in competitive markets. Moreover, it has also helped to further understand complex negotiation mechanisms between vendors and buyers.

Recently, we have noted a great rise in the popularity of auctions of various types [9]. This development occurred in many settings: in government privatizations and rights allocation (most famous is the FCC spectrum right auctions [6]) [10], [11]; in the many internet auction sites [7], [8]; in the usage of techniques from auction theory for computational resource allocation [12]; in computerized agent systems [13], [14]; and current trends in B2B e-commerce [15].

Besides the research on auction mechanisms undertaken in economics and operations research, the technology necessary to implement electronic auctions [16], [17], [18] is a research issue on its own. Agent technology has already been applied in different work [19], [20], [21], [22]. This paper concentrates on the approach of applying on agent technology in e-commerce.

The application of the multi-agent paradigm to auctions can be viewed from two different points of view:

  • 1.

    The mechanisms of an auction can be defined as a resource allocation problem to a set of agents. The available resources are limited with regard to the number of demands. The problem may thus be described as a market in which there are vendor agents and buyer agents, which trade on items represented by the resources. These agents exhibit different acquisition capabilities that let them act differently depending on the current context or situation of the market. For example, the ‘richer’ an agent is, the more items it can buy, i.e. the more resources it can acquire.

  • 2.

    The auctions can be viewed as a process of automatic negotiation implemented as a network of intelligent agents. Buyer and vendor agents interact in an electronic market environment to trade items. Such an approach is for example represented by AuctionBot [23]. Alternatively, auctions may form an integral part of a multi-agent architecture. An example of this approach is represented by the NetSA architecture [24]. In this architecture, supervisor agents associated with institutions offer a same product in competition with each other applying auction mechanisms in order to offer to a user agent the best price for the product.

The work presented in this paper focuses on the second approach where auctions are considered as a process of automatic negotiation applying the multi-agent paradigm. In the Section 2, we explain how we see auctions for automatic negotiation between agents. Section 3 presents a model for multi-item auctions. The strategy and equilibrium conditions of the auction process relying on this model are presented and analyzed in Section 4. Section 2 presents an implementation of the model. The simulation results of three typical cases are presented and discussed in Section 6. Finally, we conclude the paper in Section 7.

Section snippets

Market framework

An environment where vendors and buyers meet with the goal to sell and buy goods is commonly called a market. As there are many different interpretations of what a market is such an environment should rather be called a market framework. Fig. 1 shows an example of such a framework [25], [26], [27]. There are four cases presented:

  • 1.

    one vendor and one buyer directly negotiate in the classical sense;

  • 2.

    multiple vendors and one buyer are engaged in a reverse auction;

  • 3.

    multiple buyers and one vendor are

A multi-item auction model

We are interested in auctions that include multiple identical items. Most work on multi-item auctions suppose two simplifying conditions: the quantity of items to sell is fixed as well as the quantities requested by the buyers. These two hypothesis do not meet the requirements of many situations where auctions are used. Lengweiler [34] for example proposes an auction model, where the available quantity is not fixed. It can therefore change during the auction as it is for example the case for

Strategy and equilibrium

Every participant in the auction tries to win as if it were a simple English auction. Because a participant does not know which are the quantities asked for by the other participants, it may happen that his bid will be out-done by other buyers. It is thus faced with the risk that the demanded quantity qi will be entirely allocated to another buyer offering a higher price. The buyer is always faced with the dilemma where he wants to minimize his bid bi to maximize his gains, but where on the

Simulation

The model presented in the Section 4 has been implemented as a simulation platform based on the multi-agent paradigm.

Empirical evaluation

This section presents and discusses empirical results obtained by the simulation of the model described in this paper. Three different cases are evaluated.

Case 1

Same needs and same budgets

Suppose there are 10 items to sell and n=5 buyer agents. All the buyers A1…5 dispose of similar amounts of money to spend (ViVminVmax,1≤i≤5). The initial quantity each buyer Ai asks for is equal to 10 items (qi=10,1≤i≤5), and the minimum quantity accepted by the vendor agent shall be 6 items. The strategies of the

Conclusion

In this paper we discussed the multi-agent paradigm and its application to multi-item auctions. We proposed a formal model for auction based automatic negotiations. This model has been implemented using MAS and was tested and evaluated with simulation experiments. Recently, much work on multi-item auctions have addressed the combinatorial issue that allows bids on combinations of items as opposed to only single items. These approaches suppose however, two simplifying conditions: the quantity of

Acknowledgements

This work was partially supported by the Canadian Natural Sciences and Engineering Research Council (NSERC).

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