Can intermediaries assure contracts? Experimental evidence

Abstract We model economic transactions as prisoner's dilemma games with an outside option played by randomly matched pairs drawn from an anonymous population. In this environment, two intermediary institutions are studied who punish their customers for cheating. One institution does so by enforcing payment of a fine, while the other inflicts a bad reputation on the customer. By voluntarily becoming a customer of an intermediary institution, a player can signal her pre-commitment to honest action to the transaction party. The paper reports experimental results, which show that such a pre-commitment practice fosters cooperation and improves efficiency relative to the setting without intermediation. The results show that when the intermediary imposes a fine on customers for cheating, behavior moves towards the social optimum. In contrast, when the intermediary has only a mandate to impose a bad reputation score on cheating customers, efficiency gains are small compared to a situation without any intermediary.


Introduction
In (almost) all bilateral economic transactions both trading parties have an opportunity to make a gain at the expense of the other. A seller can cheat on quality; a buyer can cheat on payment. When they fear a loss from fraud, prospective market participants may avoid transactions that would be mutually beneficial. They need contractual assurance promoting both honest play and trust in the transaction. In markets where no law allocates contractual assurance, private intermediation has established as an alternative mode of governance. Intermediary institutions have evolved either in decentralized or in monopolistic structures. Feedback forums on computer platforms in Internet markets (Resnick et al., 2000) and 'gossip networks' in emerging markets (McMillan and Woodruff, 2000) induce a decentralization of intermediation. Monopolistic structures of intermediation dominate, for instance, in the shadow economy (Gambetta, 1993). In India, the non-profit organization Janaagraha established 2010 the website IPaidABribe, where citizens can report actual corrupt acts. Regions obtain a bad reputation when frequent reports of bribes emerge. Local governments face then political pressure to improve measures against corruption. Ryvkin et al. (2017) model a comparable information-sharing system and investigate it in the laboratory. Their results suggest that the mere existence of an intermediary institution like IPaidABribe is insufficient to systematically lower bribery. Additional requirements on the quality of information are necessary to improve efficiency. Cason et al. (2016) report on experiments analyzing the impact of social information schemes for achieving compliance. Akin to the results of Ryvkin et al. (2017), Cason et al. (2016) observe frequent misreporting which undermines the efficiency of a feedback institution.
The service intermediary institutions offer to transaction parties consists either in the dissemination of information on past cheating or in enforcement actions. 2 The theoretical literature suggests that information unveiling cheaters and the punishment of cheaters are crucial ingredients to inducing honest play in a population (Dixit, 2003). This paper is inspired by Dixit's model and reports on a laboratory study that investigates the efficiency enhancing effect of two highly stylized intermediary institutions, referred to as INFO and ENFO. INFO records and disseminates information about past cheating. In contrast, ENFO may enforce a fine on cheaters. Neither INFO nor ENFO have legal mandates to punish cheaters. Individuals become voluntarily customers of an institution or not. The subsequent economic transaction is modeled as a prisoner's dilemma game (PDG) featuring an outside option. This outside option is embedded in the model to control for the influence of the intermediary institutions on the frequencies of transactions and not only on the outcomes of transactions. It accounts for the fact that people cannot usually be forced to agree to a contract and that they have the right to refuse any particular transaction party. A customer of an intermediary institution unilaterally pre-commits to receiving a determined punishment for cheating in the PDG. Therefore, the present study also contributes to the literature on the resolution of the PDG (e.g., Kreps et al., 1982;Kandori, 1992;Ellison, 1994;Nowak and Sigmund, 1998a,b;Dixit, 2003). The pre-commitment option to become a customer of the intermediary institution contrasts with the laboratory institutions of reputation and enforcement available in the literature, which establish participation by default. 3 Only Andreoni's (2005) nonbinding optional satisfaction guarantee treatment may have similar degrees of freedom as our institutions. We propose to study the pre-commitment options as well as the outside option because such options are realistic features of contract assurance.
Feedback reputation systems in person-to-person online auction markets 4 and credit-rating agencies perform a similar contract assurance task as INFO. ENFO involves an economic assurance comparable to contractual liability or collateral which imply accountability in case of contract breach. Treaties involve liabilities to which willing countries agree under international law. Satisfaction guarantees are voluntary liabilities of sellers to enthrall buyers. Collaterals like dead pledge, mortgage or bail are usually compulsory to the contract and requested on a take-it-or-leave-it basis, but the contract taker still accepts them voluntarily. A striking example of collaboration amid voluntary enforcement comes from China before the communist regime, where independent riverboat pullers agreed to hire a monitor to whip them in case of weak effort, as reported in Cheung (1983, p. 8).
We report the experimental results related to five treatments: a baseline treatment without an intermediary institution, and two treatments for ENFO as well as for INFO. The two treatments for the same kind of institution differ in only one parameter value as explained in Section 2. The main results can be summarized as follows. First, both institutions increase the probability of transactions and the number of efficient outcomes compared to the baseline treatment. Second, given the chosen parameter values of our treatments, ENFO's welfare enhancing effect is greater than that of INFO. Third, over time behavior slowly moves towards the social optimum under ENFO, but under INFO behavior slowly moves towards the inefficient non-cooperative solution. Fourth, in the ENFO treatments a larger fine improves efficiency more than a smaller one. These results suggest that privately organized intermediary institutions between potential trading partners could boost welfare, but outcomes are highly sensitive to institutional design and to parameter values. In this respect, our results for a rather general approach resemble the results of both Cason et al. (2016) and Ryvkin et al. (2017) for specific situations.
The paper is organized as follows. Section 2 presents the experimental design and explains the specifications of the INFO institution and the ENFO institution. Section 3 states testable hypotheses based on theoretical considerations and findings of the experimental literature. Results are presented in Section 4. Section 5 concludes, discusses the implementation of intermediary institutions, and proposes directions for further research.

Experimental design
The paper reports on five treatments to which we refer hereafter as BASELINE, ENFO(10), ENFO(20), INFO(0) and INFO(.5). 5 The experiments were conducted at the universities of York (UK) and Hannover (Germany). They were computerized using the software package z-Tree (Fischbacher, 2007) and z-tree unleashed (Duch et al., 2020). A total of 240 2 In reality, punitive measures against cheaters involve monetary fines, exclusion from transactions by boycott (Greif, 1993;Clay, 1997), blacklisting (Weidenbaum and Hughes, 1996), or ostracism (Hirshleifer and Rasmusen, 1989). 3 Reputation effects have been studied for example in the PDG (Hauk, 2003;Hauk and Nagel, 2001;Riedl and Ule, 2003;Cassar, 2007), in the image scoring game (Wedekind and Milinski, 2000;Bolton et al., 2005;Seinen and Schram, 2006), in the trust-game (Andreoni, 2005), in a transaction game (Bolton et al., 2004;Dulleck et al., 2011), and in field experiments on the Internet (see the survey of Resnick et al., 2006). Only a few studies have dedicated to the impact of enforcement institutions on cooperation (Bohnet et al., 2001;Gneezy, 2003;Andreoni, 2005). 4 The Internet auction house eBay, among others, runs a feedback forum that allows sellers and buyers to state their satisfaction or dissatisfaction about the trading partner. Several field studies on eBay have reported that prices and demand for merchandise is greater for sellers with good reputation than for those with bad reputation or without reputation (Resnick et al., 2006). 5 We use the terms "ENFO" and "INFO" both for treatments and for institutions if no confusion is possible. subjects (5 (treatments) × 6 (cohorts) × 8 (subjects)) participated in the experiment. Subjects interacted in two-person games anonymously for 50 rounds within a cohort of eight participants. Every subject participated only in one cohort under the conditions of one treatment. Within their cohort, subjects were randomly re-matched with another in every round. Each subject was initially endowed with a balance of 600 tokens to which (potentially negative) round payoffs were added after every round. At the end of the experiment, subjects received their final balance paid out in cash. Each token was exchanged for one British Pence Sterling in York and for two Eurocent in Hannover. The average payoff was £7 and e11. The experiment lasted one hour.
BASELINE. This treatment is based on a two-player PDG. Each party i might either 'cheat' C i (frequently referred to as 'defect') or play 'honest' H i (i.e., 'cooperate'), i = 1, 2. Fig. 1a presents the PDG in normal form including the payoffs in tokens. The design involves a symmetric setting; thus, the index i denotes any of the two players. In the dominant strategy equilibrium of the PDG both players play C i and lose one token. Conversely, in the cooperative solution both play H i and win 10 tokens each. Finally, if one plays honest while the other cheats, the cheating [honest] player wins 20 [loses 10] tokens. In each of the 50 rounds an optional prisoner's dilemma (OPDG) is played. In the first stage, each player has the option to refuse or to accept to interact with the other one. Fig. 1b represents the resulting OPDG. The dashed lines in Fig. 1b indicate player 2's information sets. If at least one player chooses Refuse i , the game ends, and both players receive a zero payoff. Only if both players choose Accept i , the PDG is played out in the second stage. If the PDG is played, we say that a transaction takes place.

ENFO(10) and ENFO(20).
In these two treatments, the game extends the OPDG by inclusion of a 'pre-stage' decision to subjects' refusal option, which affects the payoffs. At that first stage of the thus constructed three-stage game, each subject decides whether to become a customer of the intermediary institution ENFO or not (see Fig. 2). A customer of ENFO must pay a fine f if she plays action C i in the PDG. A non-customer, i.e., a player who chooses No ENFO i , faces the (potential) own payoffs identical to BASELINE as presented in Fig. 1b except that the other is informed about this choice. The decision to 'buy' ENFO is independent across rounds. The two treatments ENFO(10) and ENFO(20) impose a fine of f = 10 and f = 20 on cheating customers, respectively.

INFO(0) and INFO(.5).
Analogously to ENFO, players simultaneously decide to 'buy' INFO at the first stage of the three-stage game. The game tree featuring the INFO treatments is represented in Fig. 3. Note that, also analogously to the ENFO treatment, the choice to buy INFO is independent across the rounds of the repeated game; one is a customer of the intermediary    (Wedekind andMilinski, 2000 Bolton et al., 2005;Seinen and Schram, 2006). Bolton et al. (2004) give to each player the full transaction record of the counterpart. Different from the literature, our subjects have an option as they decide on revealing information on their cheat score to the counterpart or not. 7 We use the notation "INFO i " both for individual i's choice to become a customer of the intermediary institution INFO and for individual i's sum of the five entries of his bad reputation records, if no confusion is possible. 8 Before a subject decided to buy INFO or not her bad reputation cheat score was displayed on her screen and she was reminded that buying INFO implied both: the revelation of her bad reputation cheat score INFO i to the randomly matched partner and the recording of her action in the PDG.

Hypotheses
In this section, we state testable hypotheses for the outcomes of the five treatments. The predictions resulting from the assumption of fully rational behavior are easily obtained by backward induction. Hypothesis 4. There are no behavioral differences between ENFO(10) and ENFO(20).
For many games of interest, subgame perfectness is a weak predictor of actual behavior as the experimental literature shows (e.g., Selten and Stoecker, 1986). Therefore, a rejection of Hypotheses 1 or 4 would not be surprising, but it also should not be the end of our story. Some models (e.g., contagious punishment with homogeneous agents; Kandori, 1992;Ellison, 1994) show that cooperation can arise in the PDG with anonymous matching. 10 Experimental evidence suggests that several possible sources for cooperation exist in the OPDG. First, the option to refuse may be used more frequently by non-cooperative subjects because they expect to be cheated by the others, too (Orbell and Dawes, 1993;Hauk, 2003;Hauk and Nagel, 2001). Second, the great surplus of mutual honest play relative to mutual play of cheat (Rapoport and Chammah, 1965) and the negative payoffs for mutual play of cheat have been reported to foster cooperation (Hauk, 2003). Finally, a 'partner' framing is used in the instructions (see the online appendix (section B)). Burnham et al. (2000) show that such a framing may raise cooperation levels. These findings suggest the following hypothesis.
Hypothesis 5. If subjects forego the option to refuse and a transaction takes place, they play honest, independent of the treatment.
Results of laboratory and field experiments suggest that high cooperation levels are possible within frameworks related to INFO. First, in the repeated multiple-players PDG, information feedback on each player's past behavior can induce high cooperation levels (Hauk, 2003;Hauk and Nagel, 2001;Riedl and Ule, 2003; for a literature survey, see Kosfeld, 2004). Subjects who play honest in the past are preferred future partners; they may associate in small subgroups and refuse to play with others who previously cheated. Second, in experiments with the image scoring game where one can either help (being the efficient collective action) or hurt, feedback on past actions significantly increased helping levels (Wedekind andMilinski, 2000 Seinen andSchram, 2006;Bolton et al., 2005). Third, in an experiment with a closely related sequential transaction game in which a buyer submits a payment or opts out and the seller decides to ship or not, Bolton et al. (2004) report a positive effect of reputation feedback on cooperation compared to the benchmark of random matching without reputation. Finally, several field studies on Internet markets also suggest that the goodness of a seller's reputation 9 For a customer of ENFO (10)    is positively correlated with demand for her goods and the auction prices she earns (see the survey of Resnick et al., 2006). However, Dulleck et al. (2011) find in experimental markets for credence goods little influence on efficiency when sellers can build up reputation.
A customer of INFO can build up reputation on account of her past behavior. If transaction parties only accept customers with good reputation (i.e., zero cheat score), these are better off. We introduce the honest strategy as follows: 11 The proposal that the honest strategy may evolve through reputation will be referred to as the 'reputation theory' 12 hereafter. The reputation theory could contribute to explain behavior if the following hypothesis is rejected:

Experimental results
Table 1 surveys the average round payoffs (in tokens), the relative frequencies of average behavior for all treatments, and the corresponding independent group observations. The relative frequencies of the resulting game outcomes for the five treatments are illustrated in Fig. 4. 14 To test Hypotheses 1 to 5, we first perform 32 OLS dummy-regressions across session averages using the following dummy variables: 11 The honest strategy reads: "buy INFO; accept the PDG given the other is a customer with a zero bad reputation cheat score, otherwise refuse; as a customer, play H i at the third stage, as a non-customer, play C i ." 12 In contrast to the reputation theory, the reciprocity theory (Nowak and Sigmund, 1998a,b) proposes a social tit-for-tat strategy: the society rewards honest players for their exemplary behavior in the past and sanctions cheaters by exclusion. Therefore, opportunists mimic the tit-for-tat type in the economy. Note that indirect reciprocity and reputation theory suggest playing the honest strategy based on a different rationale. While in the reputation theory agents refuse to play the PDG with a non-customer or a past cheater to protect herself against abuse, the social tit-for-tat type chooses Refuse i to punish past cheaters. 13 The goodness of reputation records is ordered as follows, INFO i = {0, 1, >1, No INFO i }. Non-customers are considered of having the worst reputation.
More than one, one and zero revealed records are better, still better and best, respectively. 14 Figures A1-A3 in the online appendix (section A) present the evolution of these frequencies for the treatments plotted over time in intervals of ten rounds. Likewise we illustrate in A4 the evolution of the INFO reputation scores. The raw data are provided in the appendix (section C) of the supplementary online material.
If the regression contains all 30 sessions (6 observations × 5 treatments), we include two or four dummy variables. If the regression contains the 24 sessions with intermediary institutions we consider either one or three dummy variables. Finally, if the regression includes 12 sessions of the INFO [ENFO] treatments, we consider one dummy variable for the differential treatment effect. The variables of columns (2), (3), (4), (6), (7), and (8) of Table 1 represent the dependent regression variables, Y k . We report the regression results in Table 2, numbered from 1 to 32. In view of the Hypotheses 1 to 5, we summarize the outcomes of the regressions in the following Results 1 to 5, respectively.
Result 1. a) In all treatments, subjects choose to accept (i.e., choose to enter the PDG) more frequently than refuse. Hypothesis 1a) must be rejected (see regressions 5 and 6). b) Subjects tend to become customers of the existing intermediary institutions INFO and ENFO. Hypothesis 1b) must be rejected (see regressions 1-3 and 5-9). c) Subjects in ENFO tend to behave in line with subgame perfectness. Hypothesis 1c) is weakly supported (see regressions 1, 2, 4-8, and 10), but not strictly. 15 Result 2. In ENFO the relative frequency of choosing to accept is significantly greater than in BASELINE (see regression 5) and in INFO. Hypothesis 2 cannot be rejected (see regression 7). Result 4. The relative frequency of honest play (see regression 20), the conditional frequency for honest play given that the PDG is played (see regression 26), and the subjects' payoff (see regression 32) are significantly greater in ENFO(20) than in ENFO (10). For the other three variables under consideration, there is no significant difference between ENFO(10) and ENFO(20). Hypothesis 4 must be partly rejected (see regressions 4, 10, and 14). See also Result 4' below.
Result 5. In ENFO the relative frequency of honest play in the PDG is significantly greater than in BASELINE (see regression 21) and in INFO (see regression 23). Furthermore, this relative frequency is also significantly greater in INFO than in BASELINE. Hypothesis 5 must be rejected (see regression 21).
To test Hypothesis 6 (i.e., the conjecture that reputation plays no role in INFO), we draw on the conditional frequencies of decisions when matched with a customer or a non-customer of INFO. We consider four reputation conditions for each subject (non-customer, customer with zero, one, or more than one bad reputation records) and the 16 possible combinations of these reputation conditions. Before constructing the test of Hypothesis 6, we revisit Hypothesis 3. For each of the 64 conditional relative frequencies presented in Fig. 5 (16 bars × 4 segments) we conduct pairwise tests between INFO(0) and INFO(.5). Most differences across these treatments are not significant, but some significant differences exist, thus, elucidating the Result 3 that Hypothesis 3 must partly be rejected.

Result 3'. The main behavioral difference between the treatments INFO(0) and INFO(.5) arises from situations where at most one player chooses the intermediary institution. 16
We test Hypothesis 6 for the conditional likelihood of the H i choice both treatments against the alternative hypothesis with at least one inequality being strict. In Table 3 We test for i = j (Hypothesis 6a)) and for i = j = −i (Hypothesis 6b)). For the test of the conditional likelihood of the Accept i choice (Accept i replaces H i in the chain of ordered alternatives), the inequality signs remain the same for i = j, but are reversed for i = j. The four Page tests of ordered alternatives all reject the null hypotheses in favor of the alternative hypotheses. We report the test results in Table 3 for both treatments INFO(0) and INFO(.5). Therefore, we obtain the following: Result 6. In both INFO treatments, subjects' choices depend on the goodness of one's own reputation score and the reputation score of the opponent. Hypotheses 6a) and 6b) must be rejected. 15 In regressions 5-8 and 10, the relative frequency of accepting is not only significantly different from 0%, but also from 100% at the 1%-level. 16 Conditionally on the other player choosing No INFO j , more subjects in INFO(.5) choose to refuse the PDG than in INFO(0), (p = .037, n 1 = n 2 = 6, Mann-Whitney test). One other interesting difference between the two treatments can be anticipated from .003 * * * .005 * * * a We test the null hypothesis * * * p < .01, * * p < .05, * p < .1; j = −i denotes the other player j = i.
Top: non-customers (No ENFO i ); Bottom: customers (ENFO i ). # indicates relative frequency of matching. Left: ENFO(10); Right: ENFO(20). The bar charts show the relative frequencies (in %) of outcomes: H-honest; C-cheat; i/j Refuse-second stage refusal, where i Refuse includes the cases when both players refuse to play. As shown in the top row for ENFO(10), non-customers i were matched with non-customers j in #11% of all cases. In these occasions, non-customers played H i in 11% and C i in 61% of times. In 28% of these occasions the PDG was not reached; in 24% (= 2 × 12%) one non-customer (either i or j) refused and in 4% (= 16% − 12%) both non-customers refused. For the ENFO institution, we report in Fig. 6 the conditional decisions of customers (bottom diagrams) and non-customers (top diagrams) when matched with a customer (left bar) or a non-customer (right bar). The recorded numbers represent the conditional relative frequencies (in %) for the 'row player' i given that the other player j is a customer or a non-customer. The left diagrams record these frequencies for ENFO(10) and the right ones for ENFO(20), respectively. On top of each bar the relative frequency of the corresponding matches is displayed.
Most differences across these treatments are not significant, but some significant differences exist, thus, elucidating the Result 4 that Hypothesis 4 must partly be rejected. Result 4'. Customers of ENFO(10) play cheat more frequently than customers of ENFO(20) when matched with a noncustomer and when matched with a customer. 17 Hence, Hypothesis 4 must partly be rejected.
Other conditional frequencies as represented in Fig. 6 are not significantly different at the 10% level between the two ENFO treatments.
To test Hypothesis 7 (i.e., no repetition effect), we conduct OLS regressions on the time trend with robust standard errors. As before, the dependent regression variables are the relative frequencies of playing H i and C i (all treatments), Accept i (BASELINE treatment), Accept i when being a customer (INFO or ENFO treatments), and Accept i when being no customer within the respective round. Table 4 shows the results for all five treatments. Hence, we report the following result: Result 7. a) In BASELINE, the relative frequencies of Accept i and of H i are significantly decreasing and the relative frequency of C i is significantly increasing with repetition. -Hypothesis 7a) must be rejected. b) In INFO(0), the relative frequencies of Accept i , No INFO i and of H i are significantly decreasing and the relative frequency of C i is significantly increasing with repetition. -Hypothesis 7b) must be rejected. c) In INFO(.5), the relative frequency of Accept i , No INFO i are significantly decreasing and the relative frequency of C i is significantly increasing with repetition. -Hypothesis 7c) must be rejected.   (0) after 20 periods; that's when subjects with a good reputation score buy INFO despite the cost.

Discussion and conclusion
The paper reports experimental evidence for the impact of contractual assurance through intermediation on behavior in the PDG with random matching involving the option to refuse. The data show that efficiency increases relative to the situation without any intermediary institution. Two different intermediary institutions were investigated. The ENFO institution collects fines from cheaters among its customers, whereas the INFO institution earmarks bad behavior of its customers but also enables them to build up good reputation. The ENFO treatments produced higher payoffs and cooperation levels than the INFO treatments. Subjects in the ENFO institution used the option to refuse significantly less frequently than the subjects in the INFO institution. Customers of ENFO were evidently more trusted by transaction parties than customers of INFO. This trust is clearly based on observed actions; subjects in ENFO choose honest play more frequently and thus earn a higher payoff than those in INFO. These differences between the treatments favor ENFO over INFO from the viewpoint of contractual assurance.
However, the considered institutions ENFO and INFO could not completely resolve the prisoner's dilemma in the laboratory. The outcomes with ENFO only moved slowly towards the cooperative outcome, and the outcomes with INFO moved towards the non-cooperative outcome rather than to the cooperative one. At first glance, this discrepancy seems to correspond to the conjecture that people learn to behave according to the rationality of backward induction. Due to our parameter choices, cooperation is the result of the subgame perfect equilibrium with ENFO, but with INFO no transaction takes place in equilibrium. But a closer look at some subgames shows that backward-induction rationality is often violated.
In order to work out sharper results it seems necessary to conduct further experiments with different parameters. First, in the OPDG a kind of "gambling" is very tempting. If the costs c to become a customer of INFO is small like in our experiments, the bet of winning sometimes 20 -c and losing sometimes 1 + c is very attractive in comparison with repeated zero. A few "gamblers" undermine the trust into the emerging institution INFO. Higher losses for mutual cheating may favor the exercise of the option to refuse. Second, to become a customer of ENFO is no longer a dominant strategy if for the fine f < 10 holds. To change the parameters in both indicated directions is more level playing field for a comparison of the impacts of ENFO and INFO.
The height of the fine is fundamental when the ENFO institution is about to be implemented in practice. The levels f = 10 and f = 20 evidently disciplined the customers of ENFO in the experiment and increased cooperation. One may ask the question; is a higher fine always a better one? The relevant problem to the practical implementation is that the required deposit binds liquidity and may deter many potential entrants from participation. How many customers an Internet auction house such as eBay would attract if the customers had to deposit a significant amount of money beforehand? Certainly, one could try to implement the ENFO institution without a deposit. But if the potential fine is not deposited in advance it is likely that the cheater does not submit the fine when caught cheating. An example of non-compliance with an enforcement institution comes from the European Union. Its Stability and Growth Pact (SGP) requires the deposit of a fine for violating the conventions. France and Germany violated the SGP, but they refused to pay the fine. Finally, they were freed. Since INFO requires no deposits, it is less capital demanding and thus rather feasible, e.g. for a start-up business. This issue may account for the fact that information intermediary institutions develop frequently in emerging markets. With a glance at our results, the question arises: How can these markets exist based on information intermediation? To answer this question, one must contemplate the differences between the empirical markets and our experimental design. In the latter, punishment on cheaters was decentralized by refusal from individuals in the population. In contrast, information institutions in empirical markets usually involve a centralized punishment by expulsion. For instance, the Internet company eBay dismisses customers who have a certain number of bad reputation records. The institution involves thus both, inexpensive information and a credible threat of punishment. It is possible that private information intermediation needs centralized punishment rather than a decentralized one to support cooperation. 18 Another important point is the reliability of provided information. The experimental results of Cason et al. (2016) and Ryvkin et al. (2017) show that widespread misreporting can undermine the functioning of an INFO-like institution. In our experiment, information conveyed is completely safe, but it turns out that this is insufficient to ensure a good performance of INFO. A different sequential game structure (see Clark and Sefton, 2001) may help to foster cooperation in the INFO institution. Possibly a full record of past play might affect a more serious concern for reputation on the side of cheaters, too. In the presented design the small number of possible reputation records enabled a quick recovery of an impeccable reputation at any time. Another idea to improve the performance of INFO is a design in which the costs to become a customer are only incurred if and only if a transaction takes place.
The focus of this paper has been on cooperation and efficiency. The considered intermediary institutions were precise, unbiased and incorrupt. Private institutions may not necessarily match this picture but rather be interested in maximizing their own profits. Thus, one question of concern is: to what extent can a profit maximizing intermediary extract the benefits from the players of the game? 19 In light of our data, it seems that the intermediary institution may indeed extract some welfare if the fee is small but also deter some customers. For INFO we observed an apparent trade-off between the service cost and the number of customers and for ENFO between the height of the fine and honest play; an increase of ENFO's fine induced lower earnings of the intermediary and a significant increase of honest play. This trade-off between the intermediary's income and welfare poses another interesting direction for future research.