Renegotiation in Repeated Games with Side-Payments

We consider repeated games with side-payments: players have an endowment of wealth in each period in which transfers can be made. We show that if endowments are large enough and the common discount factor high enough, then a strongly renegotiation–proof equilibrium (SRP) in the sense of Farrell and Maskin exists. As the discount factor goes to 1, the set of SRP payoffs converges to the set of efficient, individually rational payoffs. These results provide a justification for the efficiency principle when agreements are not enforceable. Journal of Economic Literature Classification Numbers: C73, D23, L14.     

Repeated Games with Bounded Entropy

We investigate the asymptotic behavior of the maxmin values of repeated two-person zero-sum games with a bound on the strategic entropy of the maximizer's strategies while the other player is unrestricted. We will show that if the bound η(n), a function of the number of repetitions n, satisfies the condition η(n)/n → γ (n → ∞), then the maxmin value Wⁿ(η(n)) converges to (cav U)(γ), the concavification of the maxmin value of the stage game in which the maximizer's actions are restricted to those with entropy at most γ. A similar result is obtained for the infinitely repeated games. Journal of Economic Literature Classification Numbers: C73, C72.     

On Renegotiation-Proof Equilibria in Finitely Repeated Games

This paper studies renegotiation-proof equilibria of Beno?̂t and Krishna (1993) in finitely repeated games with more than two players. We provide a simple characterization of the set of average payoffs from renegotiation-proof equilibria: the limiting set of average equilibrium payoffs is either efficient or dimensionally small as the horizon of the repeated game goes to infinity. Two sufficient conditions for the former to occur are provided. An example shows that those conditions cannot be weakened.Journal of Economic LiteratureClassification Numbers: C72, C73.     

Communication in Repeated Games with Private Monitoring

The paper considers repeated games where each player can be observed by only a subset of the other players, and where players can make public announcements about the behavior of the players they observed. We address the following question: What is the minimal level of observability that is required to obtain efficient outcomes? The main result is that the limit set of sequential equilibrium payoffs, when the discount factor tends to one, contains the set of individual rational payoffs whenever each player is observed by at leasttwoother players.Journal of Economic LiteratureClassification Number: C73.     

Cost Structures and Nash Play in Repeated Cournot Games

This paper reports an experiment designed to assess the effects of a rotation in the marginal cost curve on convergence in a repeated Cournot triopoly. Increasing the cost curve's slope both reduces the serially-undominated set to the Nash prediction, and increases the peakedness of earnings. We observe higher rates of Nash equilibrium play in the design with the steeper marginal cost schedule, but only when participants are also rematched after each decision. Examination of response patterns suggests that the treatment with a steeper marginal cost curve and with a re-matching of participants across periods induces the selection of Nash Consistent responses.     

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.     

A Folk Theorem for Repeated Sequential Games

We study repeated sequential games where players may not move simultaneously in stage games. We introduce the concept of effective minimax for sequential games and establish a Folk theorem for repeated sequential games. The Folk theorem asserts that any feasible payoff vector where every player receives more than his effective minimax value in a sequential stage game can be supported by a subgame perfect equilibrium in the corresponding repeated sequential game when players are sufficiently patient. The results of this paper generalize those of Wen (1994), and of Fudenberg and Maskin (1986). The model of repeated sequential games and the concept of effective minimax provide an alternative view to the Anti–Folk theorem of Lagunoff and Matsui (1997) for asynchronously repeated pure coordination games.     

Reciprocity and Cooperation in Repeated Coordination Games: The Principled-Player Approach

Two long-lived players play a repeated coordination game. I show the restrictions on players' beliefs which imply that cooperation is optimal play. Journal of Economic Literature Classification Number: D83.     

Merging, Reputation, and Repeated Games with Incomplete Information

We relate and unify several results that appeared in the following domains: merging of probabilities, perturbed games and reputation phenomena, and repeated games with incomplete information. Journal of Economic Literature Classification Numbers: C72, D83.     

Finitely Many Players with Bounded Recall in Infinitely Repeated Games

We study the set of limit points of equilibrium payoffs in n-player repeated games, with bounded recall, when the memory capacities of all the players grow to infinity. Two main issues are explored: (i) whether differential information enables players to play correlatively, and (ii) the extent to which boundedly rational players can learn others′ behavior patterns and conceal their own. Journal of Economic Literature Classification Number: 026.     

Nash Equilibria of Repeated Games with Observable Payoff Vectors

We study a model of repeated games with imperfect monitoring where the payoff vector is observable. In this situation, any profitable deviation is detectable by all the players but the identity of the deviator may be unknown. We design collective punishments directed against the set of potential deviators. A particular class of signals is studied for which a characterization of the set of equilibrium payoffs is obtained. Journal of Economic Literature Classification Numbers: C73.     

A Property of Nash Equilibria in Repeated Games with Incomplete Information

We consider two-person non-zero-sum infinitely repeated games with lack of information on one side. The characterization of Nash equilibrium payoffs obtained by Hart allows for complex strategies, which are actually required by some equilibrium payoffs in some games. We show that appropriate one-shot public communication mechanisms make Nash equilibrium payoffs achievable by means of simple strategies. Furthermore, these mechanisms satisfy a notion of self-fulfillment.Journal of Economic LiteratureClassification Numbers: D82, C72.     

An Example of Dynamic (In)Consistency in Symmetric Extensive Form Evolutionary Games

An example is developed to show that equilibrium selection via dynamic stability, when applied to the normal form of extensive form games, is inconsistent with the subgame structure. Alternative dynamic approaches are proposed and discussed to circumvent this inconsistency. Journal of Economic Literature Classification Numbers: C70, C72.     

Population Monotonicity and Egalitarianism for Binary Social Choice Problems

We consider the class of binary social choice problems. A society must choose one of two public projects, money being available to perform side payments and each agent having quasi-linear preferences. Moulin (1987, Quarterly Journal of Economics 102 , 769–783) formulates the problem and characterizes the egalitarian solution on the basis of agreement . This axiom requires that changes in the preferences of some members of the society should affect the agents whose preferences have not changed in the same direction; all gain or all lose. In this paper, we present an alternative characterization of the egalitarian solution on the basis of population monotonicity. This axiom requires that upon the arrival of new agents, all of the original agents should be affected in the same direction; all gain or all lose.     

A comment on “Egalitarianism and efficiency in repeated symmetric games” by V. Bhaskar [Games Econ. Behav. 32 (2000) 247-262]

We identify an error in Bhaskar?s (2000) Proposition 4. We provide counterexamples to this result and demonstrate that it is not correctable.     

Free-Riding and Cooperation in Environmental Games

This paper examines the negotiation of an international environmental agreement in which different countries determine the (nonenforceable) promises of investment in clean technologies to be included in the agreement. Furthermore, it analyzes countries' optimal investment in emission-reducing technologies, considering that, in addition to the utility that a country perceives from an improved environmental quality, it is also concerned about the relative fulfillment of the terms specified in the international agreement either by itself or by others. I show, first, why countries may prefer to shift most promises of investment in clean technologies to other countries, despite the fact that these promises are usually nonenforceable by any international organization. Second, I determine countries' optimal investments in these technologies, and analyze how their particular investments depend on how demanding the international agreement is, and on the importance that countries assign to each others' relative fulfillment of their part of the treaty.     

Gradualism in Bargaining and Contribution Games

This paper identifies a source of gradualism in bargaining and contribution games. In the bargaining games we examine, each party can opt out at any time, and the outside option outcome is assumed to depend on the offers made in the negotiation phase. Specifically, we assume that (1) making a concession in the negotiation phase increases the other party's outside option pay-off and (2) the outside option outcome induces an efficiency loss as compared with a negotiated agreement. The main finding is that the mere presence of such history-dependent outside options forces equilibrium concessions in the negotiation phase to be gradual, and the degree of gradualism is characterized. The model also applies to contribution games in which the outside option may be interpreted as the option to implement a partial project using the total contributions made so far.     

Meaning and Credibility in Cheap-Talk Games

I define neologism-proofness, a refinement of perfect Bayesian equilibrium in cheap-talk games. It applies when players have a preexisting common language, so that an unexpected message′s literal meaning is clear, and only credibility restricts communication. I show that certain implausible equilibria are not neologism-proof; in some games, no equilibrium is. Journal of Economic Literature classification numbers: D83 D82 C73.     

Choice Certainty and Consistency in Repeated Choice Experiments

The main objective of this study is to examine how repeated choice affects preference learning in stated preference experiments. We test different hypotheses related to preference learning by analyzing response patterns and asking respondents in a choice experiment to report their experienced certainty when going through the choice tasks. In a split-sample test, we show that follow-up choice certainty questions are procedural invariant. The self-reported certainty results indicate that learning occurs, but econometric testing procedures do not identify any significant impact of learning effects on parameter estimates or variance across choice tasks. Additional tests of choice consistency suggest that preferences in the choice experiment are stable and coherent.