Belief-Based Equilibria in the Repeated Prisoners' Dilemma with Private Monitoring

We analyze repeated prisoners' dilemma games with imperfect private monitoring and construct mixed trigger strategy equilibria. Such strategies have a simple representation, where a player's action only depends upon her belief that her opponent(s) are continuing to cooperate. When monitoring is almost perfect, the symmetric efficient outcome can be approximated in any prisoners' dilemma game, while every individually rational feasible payoff can be approximated in a class of such games. The efficiency result extends when there are more than two players. It requires that monitoring be sufficiently accurate but does not require very low discounting when a public randomization device is available. Journal of Economic Literature Classification Numbers: C73, D82.     

论制度是博弈的结果——对诺思制度变迁理论的修正

制度是博弈的纳什均衡。一般而言,博弈主体响应获利机会,产生了对新制度的诱致性需求,开始制度创新活动。但在随后的逐利博弈中,由于利益分割的对抗性,却可能使博弈陷入囚徒困境,表现为无序竞争下的激烈的利益冲突。随着冲突的加深,各个博弈主体产生了更强烈的对新制度——合作规则的渴望,表现为制定规则的讨价还价行为,并附以实施惩罚战略的承诺,但规则往往一再被破坏,因为此时新制度尚未达到纳什均衡,因而难以被遵守。于是,人们试图寻求某种强制性措施——可置信的承诺行动,以求改变收益支付,从而改变博弈均衡,使博弈在集体理性下达到纳什均衡——即新制度最终形成。     

Collusion as public monitoring becomes noisy: Experimental evidence

This paper uses laboratory experiments to test the implications of the theory of repeated games on equilibrium payoffs and estimate strategies in an infinitely repeated prisoners' dilemma game with imperfect public monitoring. We find that subjects' payoffs (i) decrease as noise increases, and (ii) are lower than the theoretical maximum for low noise, but exceed it for high noise. Under the assumption that the subjects' strategy uses thresholds on the public signal for transition between cooperation and punishment states, we find that the best fitting strategy simply compares the most recent public signal against a single threshold.     

Recommended play and performance bonuses in the minimum effort coordination game

We use experiments to investigate the efficacy of recommended play and performance bonuses in resolving coordination failures in a stag-hunt type coordination game with multiple Pareto-ranked equilibria, often referred to as a “weak link” game. Participants routinely find it difficult to coordinate to the payoff-dominant outcome in such games. We look at performance in both fixed and randomly re-matched groups. A recommendation to the payoff-dominant outcome is successful in resolving coordination failures with fixed groups but only when this recommendation is “common knowledge” in the sense that all members of the group receive the same message and it is read out loud for everyone to hear. Resolving coordination failures is harder with randomly re-matched groups and the greatest success is achieved only upon payment of a performance bonus.     

In Defense of DEFECT

The one-state machine that always defects is the only evolutionarily stable strategy in the machine game that is derived from the prisoners' dilemma, when preferences are lexicographic in complexity. This machine is the only stochastically stable strategy of the machine game when players are restricted to choosing machines with a uniformly bounded complexity. Journal of Economic Literature Classification Numbers: C70, C72.     

The Three-Legged Race: Cooperating to Compete

In the prisoners' dilemma contest several couples play the finitely repeated prisoners' dilemma. Each time a couple cooperates, it scores a point, and a small prize is awarded to the winners. An analogue of the “folk” theorem for repeated games is obtained with subgame perfect equilibrium (SPE). Next, allowing renegotiations within each team, we study a solution concept based on renegotiation-proof equilibrium (RPE). If couples are informed about the score, no equilibrium exists. If they are not, cooperation is the unique equilibrium outcome.Journal of Economic LiteratureClassification Number: C72.     

Which hat to wear? Impact of natural identities on coordination and cooperation

As the workforce becomes increasingly diverse, motivating individuals from different backgrounds to work together effectively is a major challenge facing organizations. In an experiment conducted at a large public university in the United States, we manipulate the salience of participants' multidimensional natural identities and investigate the effects of identity on coordination and cooperation in a series of minimum-effort and prisoner's dilemma games. By priming a fragmenting (ethnic) identity, we find that, compared to the control, participants are significantly less likely to choose high effort in the minimum-effort games, leading to less efficient coordination. In comparison, priming a common organization (school) identity significantly increases the choice of a rational joint payoff maximizing strategy in a prisoner's dilemma game.     

Purification in the infinitely-repeated prisoners' dilemma

This paper investigates the Harsanyi [Harsanyi, J.C., 1973. Games with randomly disturbed payoffs: A new rationale for mixed-strategy equilibrium points. International Journal of Game Theory 2 (1), 1–23]-purifiability of mixed strategies in the repeated prisoners' dilemma with perfect monitoring. We perturb the game so that in each period, a player receives a private payoff shock which is independently and identically distributed across players and periods. We focus on the purifiability of one-period memory mixed strategy equilibria used by Ely and Välimäki [Ely, J.C., Välimäki, J., 2002. A robust folk theorem for the prisoner's dilemma. Journal of Economic Theory 102 (1), 84–105] in their study of the repeated prisoners' dilemma with private monitoring. We find that any such strategy profile is not the limit of one-period memory equilibrium strategy profiles of the perturbed game, for almost all noise distributions. However, if we allow infinite memory strategies in the perturbed game, then any completely-mixed equilibrium is purifiable.     

The Veil of Uncertainty Unveiled

A central assumption of constitutional economics is that in the process of constitutional decisionmaking the players' uncertainty about their post-constitutional positions (veil of uncertainty) serves the useful purpose of making unanimity and fairness at the constitutional level more rather than less probable. The paper argues that this assertion is false if the conventional assumption holds true that social contracts are threatened by a prisoners' dilemma incentive structure. By means of a simple two-person game-model it is shown that, if players are fully aware of all their partial interests, agreement on a Pareto-efficient rule will be the iterated dominance equilibrium of the game played at the constitutional level. A veil of uncertainty cannot do better. It may, however, induce disagreement or discrimination, if the prisoners' dilemma violates the cardinal property often assumed. This raises the question why the choice of rules which typically takes place in full knowledge of the players' post-constitutional positions poses so many problems although, from a theoretical point of view, unanimity seems so easy to achieve. Finally, it is examined, if there is any salutary role the veil of uncertainty is able to play in view of a post-constitutional prisoners' dilemma.     

应对新冠疫情冲击的货币政策国际协调

新冠疫情冲击了世界经济增长和金融市场稳定。很多国家推出极度宽松货币政策应对危机。从经典货币政策国际协调的博弈理论来看,应对本次疫情冲击的各国货币政策协调性不足,“以邻为壑”的非合作均衡效果明显。为数不多的货币政策协调也存在执行力不足、深度与广度不够、新兴市场国家话语权低等问题。在世界经济紧密联系、货币政策溢出效应加强的背景下,为了应对疫情冲击,国际组织需要创设协议和合作剩余分配机制,寻找货币政策刺激效果和防止国际资产泡沫之间的平衡,加强政策沟通和信息共享,提高新兴市场国家话语权,建设有效的应对危机的货币政策国际协调机制。中国应在“一带一路”倡议的框架下建立长期货币政策协调机制,在现有的IMF和G20等平台上发挥发达国家与新兴市场国家之间的协调桥梁作用,通过持续开展央行间技术性合作等措施参与和推进协调进程。     

MACROECONOMIC STABILIZATION POLICIES IN THE EMU: SPILLOVERS, ASYMMETRIES AND INSTITUTIONS

This paper studies the institutional design of the coordination of macroeconomic stabilization policies within a monetary union in the framework of linear quadratic differential games. A central role in the analysis plays the partitioned game approach of the endogenous coalition formation literature. The specific policy recommendations in the European Economic and Monetary Union (EMU) context depend on the particular characteristics of the shocks and the economic structure. In the case of a common shock, fiscal coordination or full policy coordination is desirable. When anti‐symmetric shocks are considered, fiscal coordination improves the performance but full policy coordination does not produce further gains in policymakers' welfare.     

Measuring Strategic Uncertainty in Coordination Games

This paper proposes a method to measure strategic uncertainty by eliciting certainty equivalents analogous to measuring risk attitudes in lotteries. We apply this method by conducting experiments on a class of one-shot coordination games with strategic complementarities and choices between simple lotteries and sure payoff alternatives, both framed in a similar way. Despite the multiplicity of equilibria in the coordination games, aggregate behaviour is fairly predictable. The pure or mixed Nash equilibria cannot describe subjects' behaviour. We present two global games with private information about monetary payoffs and about risk aversion. While previous literature treats the parameters of a global game as given, we estimate them and show that both models describe observed behaviour well. The global-game selection for vanishing noise of private signals offers a good recommendation for actual players, given the observed distribution of actions. We also deduce subjective beliefs and compare them with objective probabilities.     

The supercore for normal-form games

This paper analyzes the supercore of a system derived from a normal-form game. For the case of a finite game with pure strategies, we define a sequence of games and show that the supercore coincides with the set of Nash equilibria of the last game in that sequence. This result is illustrated with the characterization of the supercore for the n-person prisoner's dilemma. With regard to the mixed extension of a normal-form game, we show that the set of Nash equilibrium profiles coincides with the supercore for games with a finite number of Nash equilibria.     

A belief-based approach to the repeated prisoners' dilemma with asymmetric private monitoring

This paper extends the belief-based approach to the repeated prisoners' dilemma with asymmetric private monitoring. We first find that the previous belief-based techniques [T. Sekiguchi, Efficiency in repeated prisoners' dilemma with private monitoring, J. Econ. Theory 76 (1997) 345-361; V. Bhaskar, I. Obara, Belief-based equilibria in the repeated prisoners' dilemma with private monitoring, J. Econ. Theory 102 (2002) 40-69] cannot succeed when players' private monitoring technologies are sufficiently different. We then modify the previous belief-based approach by letting the player with smaller observation errors always randomize between cooperate and defect along the cooperative path of the play. We show that with vanishing observation errors, efficiency and a folk theorem can be approximated using our modified belief-based strategies.     

Behavioral spillovers in coordination games

Motivated by problems of coordination failure observed in weak-link games, we experimentally investigate behavioral spillovers for minimum- and median-effort coordination games. Subjects play these coordination games simultaneously and sequentially. The results show that successful coordination on the Pareto optimal equilibrium in the median game influences behavior in the minimum game when the games are played sequentially. Moreover, this positive, Pareto-improving spillover is present even when group composition changes across games, although the effect is not as strong. We also find that the precedent for uncooperative behavior in the minimum game does not influence play in the median game. These findings suggest guidelines for increasing cooperative behavior within organizations.     

Repetition, Communication, and Coordination Failure

We examine repetition as an institution that affects coordination failure in a game with and without pre-play communication. We use probit regression with random effects to test hypotheses regarding the frequency and form of coordination failure in the presence of repeated play versus one-shot games. Our results indicate that repetition without pre-play communication results in a lower frequency of coordination failure relative to one-shot game outcomes. This result is reversed when pre-play communication is allowed. Our evidence also suggests that repeated play coordination failures tend to be suboptimal Nash equilibria, whereas one-shot game coordination failures are disequilibria regardless of the presence of pre-play communication.     

Coordination and cooperation in local,random and small world networks: Experimental evidence

A laboratory experiment has been designed to study coordination and cooperation in games played on local, random and small-world networks. For the coordination game, the results revealed a tendency for coordination on the payoff-dominant equilibrium in all three networks, but the frequency of payoff-dominant choices was significantly higher in small-world networks than in local and random networks. For the prisoner's dilemma game, cooperation was hard to reach on all three networks, with average cooperation lower in small-world networks than in random and local networks. Two graph-theoretic characteristics—clustering coefficient and characteristic path length—exhibited a significant effect on individual behavior, possibly explaining why the small-world network, with its high clustering coefficient and short path length, is the architecture of relations that drive a system towards equilibrium at the quickest pace.     

The Economics of International Policy Coordination*

One aspect of reforming the world monetary system is the issue of designing a set of ‘rules of the game’ within which countries can pursue their own national objectives and yet which still leads to some form of global coordination of macroeconomic policies. The issue of strategic interactions between countries has recently received some analytical insights with the application of game theory to the economics literature on interdependence between countries. The purpose of this paper is to survey these recent applications of static and dynamic game theory to the question of international policy coordination. It also surveys the results of the few empirical attempts to measure the potential gains to coordination.     

Monotone Games with Positive Spillovers

A monotone game comprises the infinitely repeated play of an n-person stage game, subject to the constraint that players' actions be monotonically nondecreasing over time. These games represent a variety of strategic situations in which players are able to make (partial) commitments. If the stage games have positive spillovers and satisfy certain other conditions, then the limit points of the subgame perfect equilibria are precisely the approachable action profiles. This characterization is applied to voluntary contribution games, market games, and coordination games. Journal of Economic Literature Classification Number: C7.     

Risk attitudes and the stag-hunt game

A stag-hunt game (with the risky and safe actions) has two pure Nash equilibria that are Pareto-rankable. The risky action leads either to the Pareto-superior equilibrium (high payoff) or to out of equilibrium (low payoff) depending on the opponent’s action. Both players may want to obtain high payoff but uncertainty about the opponent’s action may prevent them to take such strategic risk. This paper investigates how information about the risk attitude of an opponent affects a player’s action choice in the stag-hunt game. I find that although a subject’s propensity to choose the risky action depends on her opponent’s risk attitude, it does not depend on her own risk attitude.