Conflict between groups of players in coupled socio-economic and ecological dynamics

Conflict among multiple groups is a major source of difficulty in environmental conservation. People are often divided into various groups that have different social factors, sometimes leading to differences in the degree to which they cooperate in environmental conservation. This obstructs the social consensus needed to solve the environmental problems. Here we study the coupled dynamics of human socio-economic choice and lake water pollution, and examine the magnitude of the difference in cooperation levels between two groups. In the model, many players choose between a costly but cooperative option and a selfish option. The former results in a reduced phosphorus discharge into the lake. Each player's choice is affected by an economic cost and social pressure. Social pressure is a psychological factor that promotes cooperation: it becomes stronger when more players in the society are cooperative (conformist tendency) and when the problem at hand is a greater concern to society. In the model, two groups sometimes show large differences in their cooperation levels even when both have exactly the same social factors. However, cooperation levels are more likely to differ between groups that have different social factors. Enhancement of the cross-group conformist tendency is the most effective way to minimize differences in cooperation levels and to mitigate conflict between groups.     

The optimal degree of cooperation in the repeated Prisoners' Dilemma with side payments

In the infinitely repeated Prisoners' Dilemma with side payments, we characterize the Pareto frontier of the set of subgame perfect equilibrium payoffs for all possible combinations of discount factors. Play paths implementing Pareto dominant equilibrium payoffs are uniquely determined in all but the first period. Full cooperation does not necessarily implement these payoffs even when it maximizes total stage game payoffs. Rather, when the difference in players' discount factors is sufficiently large, Pareto dominant equilibrium payoffs are implemented by partial cooperation supported by repeated payments from the impatient to the patient player. When both players are sufficiently patient, such payoffs, while implemented via full cooperation, are supported by repeated payments from the impatient to the patient player. We characterize conditions under which public randomization has no impact on the Pareto dominant equilibrium payoffs and conditions under which such payoffs are robust to renegotiation.     

On Failing to Cooperate When Monitoring Is Private

I consider a repeated prisoners' dilemma where in each period, each player receives an imperfect private signal about his opponent's current action. I show that when players are patient enough, any equilibrium where players use trigger strategies (i.e., do not revert to cooperation once they have started defecting) yields players a value arbitrarily close to the mutual minimax. I also examine the robustness of the result to perturbations of the game. Journal of Economic Literature Classification Numbers: C72.     

The folk theorem for repeated games with observation costs

The folk theorem literature has been relaxing the assumption on how much players know about each other's past action. Here we consider a general model where players can “buy” precise information. Every period, each player decides whether to pay a cost to accurately observe the actions chosen by other players in the previous period. When a player does not pay the cost, he obtains only imperfect private signals. Observational decisions are unobservable to others. Known strategies such as trigger strategies do not work since they fail to motivate players to pay for information. This paper shows that the folk theorem holds for any level of observation costs. Unlike existing folk theorems with private monitoring, ours imposes virtually no restriction on the nature of costless imperfect signals. The theorem does not use explicit or costless communication, thereby having implications on antitrust laws that rely on evidence of explicit communication. The main message is that accurate observation alone, however costly, enables efficient cooperation in general repeated games.     

Global dynamics in repeated games with additively separable payoffs

This paper studies the global dynamics of a class of infinitely repeated two-player games in which the action space of each player is an interval, and the one-shot payoff of each player is additively separable in actions. We define an immediately reactive equilibrium (IRE) as a pure-strategy subgame perfect equilibrium such that each player's action is a stationary function of the opponent's last action. We completely characterize IREs and their dynamics in terms of certain indifference curves. Our results are used to show that in a prisoners' dilemma game with mixed strategies, gradual cooperation occurs when the players are sufficiently patient, and that in a certain duopoly game, kinked demand curves emerge naturally.     

A learning-based model of repeated games with incomplete information

This paper tests a learning-based model of strategic teaching in repeated games with incomplete information. The repeated game has a long-run player whose type is unknown to a group of short-run players. The proposed model assumes a fraction of ‘short-run’ players follow a one-parameter learning model (self-tuning EWA). In addition, some ‘long-run’ players are myopic while others are sophisticated and rationally anticipate how short-run players adjust their actions over time and “teach” the short-run players to maximize their long-run payoffs. All players optimize noisily. The proposed model nests an agent-based quantal-response equilibrium (AQRE) and the standard equilibrium models as special cases. Using data from 28 experimental sessions of trust and entry repeated games, including 8 previously unpublished sessions, the model fits substantially better than chance and much better than standard equilibrium models. Estimates show that most of the long-run players are sophisticated, and short-run players become more sophisticated with experience.     

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.     

Kantian Equilibrium

Consider a game whose strategies are "contributions". A strategy profile is a Kantian equilibrium if  no  player would like  all  players to alter their contributions by the  same multiplicative factor.  Kantian equilibria are Pareto efficient. We characterize the allocation rules on several domains of environments that can be implemented as Kantian equilibria. The concept unifies the  proportional solution  on production economies and the  linear cost-share equilibrium  on public-good economies. We study Kantian equilibrium in the prisoner's dilemma, in a voting problem, and in a political economy where redistribution is the issue. The Kantian dictum engenders considerable but not unqualified cooperation.     

Gradualism and Irreversibility

This paper considers a class of two–player dynamic games in which each player controls a one–dimensional action variable, interpreted as a level of cooperation. The dynamics are due to an irreversibility constraint: neither player can ever reduce his cooperation level. Payoffs are decreasing in one&'s own action, increasing in one&'s opponent&'s action. We characterize efficient symmetric equilibrium action paths; actions rise gradually over time and converge, when payoffs are smooth, to a level strictly below the one–shot efficient level, no matter how little discounting takes place. The analysis is extended to incorporate sequential moves and asymmetric equilibria.     

Congestion games with malicious players

We study the equilibria of non-atomic congestion games in which there are two types of players: rational players, who seek to minimize their own delay, and malicious players, who seek to maximize the average delay experienced by the rational players. We study the existence of pure and mixed Nash equilibria for these games, and we seek to quantify the impact of the malicious players on the equilibrium. One counterintuitive phenomenon which we demonstrate is the “windfall of malice”: paradoxically, when a myopically malicious player gains control of a fraction of the flow, the new equilibrium may be more favorable for the remaining rational players than the previous equilibrium.     

Rational cooperation in the finitely repeated prisoners' dilemma

A common observation in experiments involving finite repetition of the prisoners' dilemma is that players do not always play the single-period dominant strategies (“finking”), but instead achieve some measure of cooperation. Yet finking at each stage is the only Nash equilibrium in the finitely repeated game. We show here how incomplete information about one or both players' options, motivation or behavior can explain the observed cooperation. Specifically, we provide a bound on the number of rounds at which Fink may be played, when one player may possibly be committed to a “Tit-for-Tat” strategy.     

Weak links, good shots and other public good games: Building on BBV

We suggest an alternative way of analyzing the canonical Bergstrom-Blume-Varian model of non-cooperative voluntary contributions to a public good that avoids the proliferation of dimensions as the number of players is increased. We exploit this approach to analyze models in which the aggregate level of public good is determined as a more general social composition function of individual gifts — specifically, as a CES form — rather than as an unweighted sum. We also analyze Hirshleifer's weakest-link and best-shot models. In each case, we characterize the set of equilibria, in some cases establishing existence of a unique equilibrium as well as briefly pointing out some interesting comparative static properties. We also study the weakest-link and best-shot limits of the CES composition function and show how the former can be used for equilibrium selection and the latter to establish that equilibria of some better-shot games are identical to those of the much simpler best-shot game.     

再生水补给的城市景观水体富营养化和生态防治

采用卫星定位方式,在S湖面选取五个观测点,对再生水补给的城市景观水体富营养化状况进行研究。结果显示,湖水中主要指标营养源CODcr.、TP、TN含量由原来的天然河水补给时9月份的峰值220、2.6、2.19（mg·L-1）分别下降到180、2.1、1.83（mg·L-1）,NH3-N含量由5月的峰值1.92（mg·L-1）下降到1.68（mg·L-1）;叶绿素和水体的PH也基本成良性发展态势,水体的富营养化得到一定的缓解。同时使用生态漂移岛为主的立体生态学复技术,对再生水补给的城市景观水体富营养化生态防治效果进行研究。研究结果表明,所选择的修复植物对水体中的富营养化指标物蓝藻和各种营养源的去除和控制率达到97%以上,实验点水质有较大改观,基本可避免城市景观水体因再生水补给带来的二次深度污染。     

Sequential two-prize contests

We study a two-stage all-pay auction with two identical prizes. In each stage, the players compete for one prize. Each player may win either one or two prizes. We analyze the unique subgame-perfect equilibrium of our model with two players where each player??s marginal values for the prizes are decreasing, constant, or increasing. We also analyze an equilibrium of the model with more than two players where each player??s marginal values for the prizes are nonincreasing.     

Inequality, cooperation, and growth: An experimental study

In a three player dynamic public goods experiment, social output today determines production possibilities tomorrow. In each period, players choose to sabotage, to cooperate, or to play best response. Sabotage harms social output and growth. Mutual cooperation maximises both. The property rights to social output are distributed unequally. Extent and skew of inequality are varied. We observe equilibrium play in most cases. There is also substantial cooperation, but little sabotage. Our exogenous variations of inequality are neutral to growth, neither negatively correlated to cooperation, nor positively correlated to sabotage. The neutrality result is shown to be sensitive to the dynamic nature of the employed game.     

Indirect higher order beliefs and cooperation

This study experimentally examines the role of indirect higher order beliefs in sequential psychological games. We consider a three-player sequential game in which the first and third players do not interact sequentially, but only through an intermediary, the second player. We posit that the third player’s decision to cooperate depends on his indirect higher order belief, namely, his belief about what the first player believes the second player would choose. We employ pre-play communication between the first and third players as a way to influence the third player’s indirect higher order belief. The evidence demonstrates that communication can effectively induce cooperation from the third player by shaping his indirect higher order belief.     

Nash equilibrium without mutual knowledge of rationality

Summary. In a Nash equilibrium, players' rationality is mutual knowledge. However, both intuition and experimental evidence suggest that players do not know for sure the rationality of opponents. This paper proposes a new equilibrium concept, cautious equilibrium, that generalizes Nash equilibrium in terms of preferences in two person strategic games. In a cautious equilibrium, players do not necessarily know the rationality of opponents, but they view rationality as infinitely more likely than irrationality. For suitable models of preference, cautious equilibrium predicts that a player might take a “cautious” strategy that is not a best response in any Nash equilibrium. Received: January 28, 1998; revised version October 2, 1998     

Dissertation abstract: Essays on veto bargaining games

This dissertation experimentally analyzes the outcomes of multilateral legislative bargaining games in the presence of a veto player. The first essay examines veto power—the right of an agent to unilaterally block decisions but without the ability to unilaterally secure his/her preferred outcome. Using Winter’s (1996) theoretical framework, I consider two cases: urgent committees where the total amount of money to be distributed shrinks by 50% if proposals do not pass and non-urgent committees where the total amount of money shrinks by 5% if proposals do not pass. Committees with a veto player take longer to reach decisions (are less efficient) than without a veto player and veto players proposals generate less consensus then non-veto players proposals, outcomes on which the theory is silent. In addition, veto power in conjunction with proposer power generates excessive power for the veto player. This suggests that limiting veto players’ proposer rights (e.g., limiting their ability to chair committees) would go a long way to curbing their power, a major concern in committees in which one or more players has veto power. Finally, non-veto players show substantially more willingness to compromise than veto players, with players in the control game somewhere in between. I relate the results to the theoretical literature on the impact of veto power as well as concerns about the impact of veto power in real-life committees. The second essay discusses in detail the voting patterns in the veto and control games reported in the first essay. The empirical cumulative density functions of shares veto players accepted first degree stochastically dominates that of shares for the controls and the empirical cdfs of shares the controls accepted first degree stochastically dominate that of shares for non-veto players. Random effect probits support this conclusion as well. In addition, regressions imply favorable treatment of voting and proposing between non-veto players which, however, does not result in larger shares in the end. Coalition partners consistently demand more than the stationary subgame perfect Nash equilibrium share except for veto players in non-urgent committees. JEL Classification C7, D7, C78, D72 Dissertation Committee: John H. Kagel, Advisor Massimo Morelli Alan Wiseman Stephen Cosslett     

EQUILIBRIA IN NON-COOPERATIVE GAMES II: DEVIATIONS BASED REFINEMENTS OF NASH EQUILIBRIUM

In any Nash equilibrium no player will unilaterally deviate. However, many games have multiple Nash equilibria. In this paper, we survey some refinements of Nash equilibria based on the hypothesis that any player may consider a deliberate deviation from a Nash equilibrium vector while expecting other players to respond optimally to this deviation. The concepts studied here differ in the expectations players have about other players' responses to a deviation. This sort of deviations philosophy is predicated on the thought process of players. Therefore, the validity of a particular equilibrium concept to an economic model may depend upon the relevance of the thought process implied by the concept.