Introduction to Repeated Games with Private Monitoring

We present a brief overview of recent developments in discounted repeated games with (imperfect) private monitoring. The literature explores the possibility of cooperation in a long-term relationship, where each agent receives imperfect private information about the opponents' actions. Although this class of games admits a wide range of applications such as collusion under secret price-cutting, exchange of goods with uncertain quality, and observation errors, it has fairly complex mathematical structure due to the lack of common information shared by players. This is in sharp contrast to the well-explored case of repeated games under public information (with the celebrated Folk Theorems), and until recently little had been known about the private monitoring case. However, rapid developments in the past few years have revealed the possibility of cooperation under private monitoring for some class of games. Journal of Economic Literature Classification Numbers: C72, C73, D43, D82, L13, L41.     

Feedback,punishment and cooperation in public good experiments

A number of studies have shown that peer punishment can sustain cooperation in public good games. This paper shows that the format used to give subjects feedback is critical for the efficacy of punishment. Providing subjects with information about the earnings of their peers leads to significantly less cooperation and lower efficiency compared to a treatment in which subjects receive information about the contributions of their peers. This is despite the fact that the feedback format does not affect incentives. The data suggest that this happens because the feedback format acts as a coordination device which influences the contribution standards that groups establish.     

Imitation with asymmetric memory

Models of learning in games based on imitation have provided fundamental insights as the relevance of risk-dominance equilibria or perfectly competitive outcomes. It has also been shown, however, that the introduction of nontrivial memory in those models fundamentally alters the results. This paper further considers the effect of asymmetric memory length in the population. We focus on two classical results and find that, while asymmetric memory crucially affects equilibrium selection in coordination games, it reinforces the stability of perfectly competitive outcomes in oligopoly games. The latter result is generalized to aggregative games and to finite population ESS in symmetric games.     

Efficiency versus collusion: a reformulation of the Weiss test

The weiss test has been used to discriminate between the efficiency and collusion hypotheses. Using a conventional oligopoly model, we show that the test is valid for the former hypothesis but not the latter. Contrary to recent emperical studies, we find that a negative coefficient on concentration in profitability equations does not refute the collusion hypothesis. In fact, this finding supports the hypothesis if the sample is dominated by small firms.     

Voluntary contributions by consent or dissent

We study games where voluntary contributions can be adjusted until a steady state is reached. In consent games contributions start low and can be increased; in dissent games contributions start high and can be decreased. The equilibrium prediction is free riding in consent games but as much as social efficiency in dissent games. We test it experimentally and confirm that the dissent mechanism yields substantial welfare improvements over the consent mechanism. With experience, subjects contribute on average less than 30% of the endowment in consent games but more than 60% in dissent games. Generally, subjects match the lower of the opponents' contributions: they do not follow when single opponents increase contributions in consent games, but follow when single opponents decrease contributions in dissent games. This asymmetry in the conditional cooperation is predicted by heterogeneity of egoistic and inequity averse types, with individual types being private information.     

Does information transparency decrease coordination failure?

We test the effect of information transparency on the probability of coordination failure in games with finite signals. Prior theory has shown that the effect of information transparency is ambiguous. Our study is based on two insights. Where signal space is finite, increased transparency usually destroys uniqueness of equilibria; and increasing transparency can reverse the risk-dominance ordering of equilibria. Our experiments show that increasing transparency improves coordination only when transparency makes the efficient equilibrium risk dominant. Coordination is degraded when increased transparency causes the secure equilibrium to be risk dominant. These results are consistent with subjects holding level-1 beliefs.     

Transparency on the consumer side and tacit collusion

This paper investigates the effects on tacit collusion of increased market transparency on the consumer side of a market in a differentiated Hotelling duopoly. Increasing market transparency increases the benefits to a firm from undercutting the collusive price. It also decreases the punishment profit. The net effect is that collusion becomes harder to sustain. In the limiting homogeneous market, the effect vanishes. Here market transparency does not affect the possibilities for tacit collusion.     

Strategic Complements, Substitutes, and Ambiguity: The Implications for Public Goods

We examine the effect of ambiguity in symmetric games with aggregate externalities. We find that ambiguity will increase/decrease the equilibrium strategy in games with strategic complements/substitutes and positive externalities. These effects are reversed in games with negative externalities. We consider some economic applications of these results to Cournot oligopoly, bargaining, macroeconomic coordination, and voluntary donations to a public good. In particular we show that ambiguity may reduce free-riding. Comparative statics analysis shows that increases in uncertainty will increase donations, to a public good. Journal of Economic Literature C72, D81, H41.     

Confusion and learning in the voluntary contributions game

We use a limited information environment to assess the role of confusion in the repeated voluntary contributions game. A comparison with play in a standard version of the game suggests, that the common claim that decision errors due to confused subjects biases estimates of cooperation upwards, is not necessarily correct. Furthermore, we find that simple learning cannot generate the kind of contribution dynamics commonly attributed to the existence of conditional cooperators. We conclude that cooperative behavior and its decay observed in public goods games is not a pure artefact of confusion and learning.     

Endogenous Move Structure and Voluntary Provision of Public Goods: Theory and Experiment

In this paper, we examine voluntary contributions to a public good, embedding Varian's (1994) voluntary contribution game in extended games that allow players to choose the timing of their contributions. We show that predicted outcomes are sensitive to the structure of the extended game, and also to the extent to which players care about payoff inequalities. We then report a laboratory experiment based on these extended games. We find that behavior is similar in the two extended games: subjects avoid the detrimental move order of Varian's model, where a person with a high value of the public good commits to a low contribution, and instead players tend to delay contributions. These results suggest that commitment opportunities may be less damaging to public good provision than previously thought.     

Paretian dictators: constraining choice in a voluntary contribution game

We explore individuals’ preferences over limiting the choice sets of others in an environment with externalities. Specifically, we conduct public goods games in which participants can mandate the contributions of others or restrict choices to a subset of feasible contributions levels. We find that, relative to a baseline treatment in which individuals make choices from the set of all contribution alternatives, allowing individuals to constrain the choices of others results in more efficient outcomes. We discuss these results in light of the literature on behavioral theories of reciprocity and conditional cooperation and in regards to the literature on pre-constitutional design, political institutions, and social choice.     

Some factors affecting demand withholding in posted-offer markets

Summary. Both oligopoly theory and experiments are concerned almost uniquely with sellers' behavior. Buyers' ability to exhibit non-trivial behavior in different market institutions remains unaddressed. This paper investigates the impact of three variables (number of buyers, surplus division at the market-clearing price and information revelation) on strategic and fairness-motivated demand withholding. Demand withholding and its ability to force lower prices increase as the number of buyers or the share of surplus earned by the buyers decreases. However, increasing the information revealed to subjects about the surplus inequality favoring sellers mildly facilitates collusion among sellers rather than provoking demand withholding as conjectured.     

Weak Moral Motivation Leads to the Decline of Voluntary Contributions

We develop a model that accounts for the decay of the average contribution observed in experiments on voluntary contributions to a public good. The novel idea is that people's moral motivation is “weak.” Their judgment about the right contribution depends on observed contributions by group members and on an intrinsic “moral ideal.” We show that the assumption of weakly morally motivated agents leads to the decline of the average contribution over time. The model is compatible with persistence of overcontributions, variability of contributions (across and within individuals), the “restart effect” and the observation that the decay in contributions is slower in longer games. Furthermore, it offers a rationale for conditional cooperation.     

Collusion in Dynamic Bertrand Oligopoly with Correlated Private Signals and Communication

This paper studies collusion in repeated Bertrand oligopoly when stochastic demand levels for the product of each firm are their private information and are positively correlated. It derives general sufficient conditions for efficient collusion through communication and a simple grim-trigger strategy. This analysis is then applied to a model where the demand signal has multiple random components which respond differently to price deviations. In this model, it is shown that the above sufficient conditions hold if idiosyncratic noise terms are sufficiently small. Journal of Economic Literature Classification Numbers: C72, D82.     

COMMUNICATION AND MARKET SHARING: AN EXPERIMENT ON THE EXCHANGE OF SOFT AND HARD INFORMATION

We study the role of communication in collusive market sharing. In a series of Cournot oligopoly experiments with multiple markets, we vary the information that firms can exchange: hard information—verifiable information about past conduct—and soft information—unbinding information about future conduct. We find that the effect of communication on the firms' ability to collude depends on the type of information available: Whereas market prices increase only slightly with hard information, the price raise due to soft information is substantial. Our results point to the types and contents of communication that should be of particular concern to antitrust authorities.     

Does R&D cooperation facilitate price collusion? An experiment

We examine in a laboratory experiment whether R&D cooperation facilitates tacit price collusion. For two scenarios of technological spillovers, a baseline treatment without binding contract possibilities and a contract treatment where it is possible to credibly commit to an R&D contract, are run. We find that the degree of price collusion in the contract treatments is significantly higher in periods where R&D contracts are made than in periods without contracts, and than in the baseline treatments.     

Estimating the causal effect of beliefs on contributions in repeated public good games

We use instrumental variables for estimating the causal effect of beliefs on contributions in repeated public good games. The effect is about half as large as suggested by ordinary least squares. Thus, we present evidence that beliefs have a causal effect on contributions, but also that beliefs are endogenous. We compare the causal, belief-based model of contributions to alternative models based on matching the previous contributions of others and responding to one’s deviation from the average in the previous round. The causal, belief-based model performs well, indicating that beliefs have a central role in determining contributions.     

Bayesian Estimation of Entry Games with Multiple Players and Multiple Equilibria

Entry game models are often used to study the nature of firms' profits and the nature of competition among firms in empirical studies. However, when there are multiple players in an oligopoly market, the resulting multiple equilibria have made it difficult in previous studies to estimate the payoff functions of players in complete information, static and discrete games without using unreasonable assumptions. To overcome this difficulty, the present paper proposes a practical estimation method for an entry game with three players using a Bayesian approach. Some mild assumptions are imposed on the payoff function, and the average competitive effect is used to capture the entry effect of the number of firms. Our proposed methodology is applied to Japanese airline data from the year 2000, when there were three major airline companies, ANA, JAL and JAS. The model comparison is conducted to investigate the nature of strategic interaction among these Japanese airline companies.     

On the endogeneity of Cournot-Nash and Stackelberg equilibria: games of accumulation

We characterize equilibria of games with two properties: (i) Agents have the opportunity to adjust their strategic variable after their initial choices and before payoffs occur; but (ii) they can only add to their initial amounts. The equilibrium set consists of just the Cournot-Nash outcome, one or both Stackelberg outcomes, or a continuum of points including the Cournot-Nash outcome and one or both Stackelberg outcomes. A simple theorem that uses agents’ standard one-period reaction functions and the one-period Cournot-Nash and Stackelberg equilibria delineates the equilibrium set. Applications include contribution, oligopoly, and rent-seeking games.     

Endogenous Games and Mechanisms: Side Payments Among Players

We characterize the outcomes of games when players may make binding offers of strategy contingent side payments before the game is played. This does not always lead to efficient outcomes, despite complete information and costless contracting. The characterizations are illustrated in a series of examples, including voluntary contribution public good games, Cournot and Bertrand oligopoly, principal–agent problems, and commons games, among others.