The Manipulability of Matching Rules via Segmentation

Our matching problems feature agents with endowments facing certain division rules. At any matching, the endowments of agents are reallocated between the matched pairs according to some given division rule, and this opens doors to an iterated matching problem and rematching, and to manipulation of some matching rules via segmentation. In this form of manipulation a coalition breaks off from the rest, matches within itself and rejoins the complementary coalition for a rematching at the new endowment profile. Under certain division rules this may benefit the coalition who breaks off without hurting the complementary coalition. Furthermore, both may benefit by first matching internally and then rejoining for a new match.     

When a Precedent of Donation Favors Defection in the Prisoner's Dilemma

Abstract. In this paper, we examine the question of whether a collective activity can influence cooperation in a subsequent repeated one‐shot prisoner's dilemma (PD) game. We conduct two series of experiments. The first consists of control experiments in which 30 periods of a PD game are played, with a random rematching of the pairs in every period. In a second series of experiments, subjects first play a donation game (DG) and then the PD game. In the DG, they collectively discuss the amount of a donation to a given charity, before putting the question to an individual and anonymous vote. Cooperation levels in the PD games preceded by the DG are significantly lower than those observed in the control experiment.     

Community enforcement when players observe partners' past play

I investigate whether a large community can sustain cooperation in the repeated prisoner's dilemma by having cheaters punished not by their victims but by third parties. In the setting where players can observe their partners' past play only, I show that cooperation can be sustained by an equilibrium that has the following two properties: players choose their actions independently of their own past play, and they are indifferent between cooperation and defection at all histories. This equilibrium carries over to the finite-population setting and is robust to noise in the process of choosing actions or of recording past play.     

Voluntarily separable repeated Prisonerʼs Dilemma with reference letters

We consider the voluntarily separable repeated Prisoner?s Dilemma model in which players randomly meet and form pairs to repeatedly play Prisoner?s Dilemma only by mutual agreement. While the literature has dealt with the case of no information flow across partnerships, we consider the case in which players can issue a “reference letter” to verify at least that the partnership entered the cooperation phase. We show that such reference letters can be voluntarily provided by the partners even at some cost, and that the sheer existence of a letter shortens the trust-building periods and thus improves social efficiency.     

Cooperation in Stochastic OLG games

This paper builds on Cremer's (Quart. J. Econ. 101 (1986) 33) seminal analysis which shows that (almost) complete cooperation can be achieved as an equilibrium in a game played by overlapping generations of players if the institution in which players cooperate is infinitely lived.We analyze a similar model in which the costs of cooperation are subject to random shocks. Even if these random shocks are very small, the range of parameters for which cooperation can be sustained is decreased considerably in comparison to the deterministic case. Furthermore, we show how the efficient outcome can be approximated if the level of cooperation can be varied continuously and the cooperation technology has decreasing or constant returns to scale, while this is not possible in the case of increasing returns to scale.     

The impact of peer ratings on cooperation: The role of information and cost of rating

In this study, we experimentally analyze the effectiveness of payoff‐irrelevant peer‐to‐peer ratings as a cooperation enforcement device in a finitely repeated public goods game setting. We run two treatments that differ in the amount of information on own and others' received rating points provided to the players, whereas, in a third treatment, we analyze peer approval when assigning ratings to others is costly. In particular, we wonder whether, even under anonymity and in the absence of reputational concerns, (a) players rate others' contribution decisions in the expected direction and (b) the peer rating mechanisms under study foster cooperation and welfare. Our findings reveal that, in the two costless rating treatments, peer rating concerns lead to higher contributions and efficiency, compared to our control. Introducing a small fixed cost for assigning rating points results in a very high percentage of subjects deciding not to rate others' behavior, so that cooperation cannot be enforced.     

Bargaining and efficiency in networks

We study an infinite horizon game in which pairs of players connected in a network are randomly matched to bargain over a unit surplus. Players who reach agreement are removed from the network without replacement. The global logic of efficient matchings and the local nature of bargaining, in combination with the irreversible exit of player pairs following agreements, create severe hurdles to the attainment of efficiency in equilibrium. For many networks all Markov perfect equilibria of the bargaining game are inefficient, even as players become patient. We investigate how incentives need to be structured in order to achieve efficiency via subgame perfect, but non-Markovian, equilibria. The analysis extends to an alternative model in which individual players are selected according to some probability distribution, and a chosen player can select a neighbor with whom to bargain.     

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.     

Matching soulmates

We study iterated matching of soulmates (IMS), a recursive process of forming coalitions that are mutually preferred by members to any other coalition containing individuals as yet unmatched by this process. If all players can be matched this way, preferences are IMS-complete. A mechanism is a soulmate mechanism if it allows the formation of all soulmate coalitions. Our model follows Banerjee, Konishi, and Sönmez, except reported preferences are strategic variables. We investigate the incentive and stability properties of soulmate mechanisms. In contrast to prior literature, we do not impose conditions that ensure IMS-completeness. A fundamental result is that, (1) any group of players who could change their reported preferences and mutually benefit does not contain any players who were matched as soulmates and reported their preferences truthfully. As corollaries, (2) for any IMS-complete profile, soulmate mechanisms have a truthful strong Nash equilibrium, and (3) as long as all players matched as soulmates report their preferences truthfully, there is no incentive for any to deviate. Moreover, (4) soulmate coalitions are invariant core coalitions—that is, any soulmate coalition will be a coalition in every outcome in the core. To accompany our theoretical results, we present real-world data analysis and simulations that highlight the prevalence of situations in which many, but not all, players can be matched as soulmates. In the Appendix we relate IMS to other well-known coalition formation processes.     

A strategic implementation of the Average Tree solution for cycle-free graph games

In this note we provide a strategic implementation of the Average Tree solution for zero-monotonic cycle-free graph games. That is, we propose a non-cooperative mechanism of which the unique subgame perfect equilibrium payoffs correspond to the average hierarchical outcome of the game. This mechanism takes into account that a player is only able to communicate with other players (i.e., to make proposals about a division of the surplus of cooperation) when they are connected in the graph.     

A resolution of N-person prisoners' dilemma

Summary. The purpose of this paper is to show that cooperation is possible in N-person prisoners' dilemma if players have incomplete information on the order of their moves. We consider a modified version of N-person prisoners' dilemma in which players sequentially move in the order determined by Nature, and during the play they get some information about others. We provide an information partition and a condition of payoffs for which cooperation is attained in an equilibrium. Further, for the case that full cooperation is not attained, we examine the largest partial cooperation which is achieved in an equilibrium. Received: March 5, 1995; revised version August 11, 1996     

Reputation,Social Identity and Social Conflict

We interpret the psychology literature on social identity and examine its implications. We model a population of agents from two exogenous and well defined social groups. Agents are randomly matched to play a reduced‐form bargaining game. We show that this struggle for resources drives a conflict through the rational destruction of surplus. We assume that the population contains both rational players and behavioral players. Behavioral players aggressively discriminate against members of the other social group. The existence and specification of the behavioral player is motivated by the social identity literature. For rational players, group membership has no payoff‐relevant consequences. We show that rational players can contribute to the conflict by aggressively discriminating and that this behavior is consistent with existing empirical evidence. Our paper relates to the empirical literature which finds that social heterogeneity tends to be increasing in economic variables which we interpret as indicating inefficiency. We provide an explanation that, as social groups compete for surplus, disagreement and inefficiency can result. Our work also relates to the social conflict literature, which examines the relationship between macro level factors such as unemployment and civil disturbances. This literature finds that the amount of social conflict tends to be increasing in the inequitability of the environment.     

HELPING BEHAVIOR IN LARGE SOCIETIES

This article investigates how helping behavior can be sustained in large societies in the presence of agents who never help. I consider a game with many players who are anonymously and randomly matched every period in pairs. Within each match, one player may provide socially optimal but individually costly help to the other player. I introduce and characterize the class of “linear equilibria” in which, unlike equilibria used in the previous literature, there is help even in the presence of behavioral players. Such equilibria are close to a tit‐for‐tat strategy and feature smooth help dynamics when the society is large.     

A Common Pool Resource Game with Sequential Decisions and Experimental Evidence

We describe a common pool resource game in which players choose how much of the stock to extract in a sequential manner. There are two choices and one represents taking a larger proportion of the stock than the other. After a player makes a choice, the remaining stock grows at a constant rate. We consider a game with a finite number of alternating moves. It is shown that changes in the larger proportion of the stock that the players are allowed to take and the growth rate affect equilibrium, but have little effect on behavior in the laboratory. In addition to observing more cooperation than predicted, we observe that parameters that are strategically irrelevant affect behavior. The results of this research might help policy makers in developing adequate policies to prevent overexploitation of some natural renewable resources.     

Structural holes in social networks

We consider a setting where every pair of players that undertake a transaction (e.g. exchange goods or information) creates a unit surplus. A transaction can take place only if the players involved have a connection. If the connection is direct the two players split the surplus equally, while if it is indirect then intermediate players also get an equal share of the surplus. Thus, individuals form links with others to create surplus, to gain intermediation rents, and to circumvent others who are trying to become intermediary.Our analysis clarifies the interplay between these forces in the process of strategic network formation. First, we show that, in the absence of capacity constraints on links, it leads to the emergence of a star network where a single agent acts as an intermediary for all transactions and enjoys significantly higher payoffs. Second, we study the implications of capacity constraints in the ability of agents to form links. In this case, distances between players must be long, which induces players who are “far off” to connect in order to avoid paying large intermediation rents. A cycle network then emerges, payoffs being equal across all players.     

Public good agreements under the weakest‐link technology

We analyze the formation of public good agreements under the weakest‐link technology. Whereas policy coordination is not necessary for symmetric players, it matters for asymmetric players; however, this fails in the absence of transfers. By contrast, with a transfer scheme, asymmetry may be an asset for cooperation. We characterize various types and degrees of asymmetry and relate them to the stability of self‐enforcing agreements. Asymmetric distributions of autarky public good provision levels (also representing asymmetric interests in cooperation) that are positively skewed tend to be conducive to the stability of agreements. We show that under such conditions, even a coalition including all players can be stable. However, asymmetries that foster stability (instability) tend to be associated with low (high) gains from cooperation.     

Cooperative behavior and the frequency of social interaction

We report results from an experiment that examines play in an indefinitely repeated, two-player Prisoner's Dilemma game. Each experimental session involves N subjects and a sequence of indefinitely repeated games. The main treatment consists of whether agents are matched in fixed pairings or matched randomly in each indefinitely repeated game. Within the random matching treatment, we elicit player's strategies and beliefs or vary the information that players have about their opponents. Contrary to a theoretical possibility suggested by Kandori [1992. Social norms and community enforcement. Rev. Econ. Stud. 59, 63–80], a cooperative norm does not emerge in the treatments where players are matched randomly. On the other hand, in the fixed pairings treatment, the evidence suggests that a cooperative norm does emerge as players gain more experience.     

International Cooperation Behind the Veil of Uncertainty – The Case of Transboundary Acidification

The complexities of international environmental problems are only poorly understood. Hence, decision makers have to negotiate about abatement measures even though they do not know the 'true' model of the ecological system and have only a rough idea about the costs and benefits of their action. It will be analysed to what extent this kind of 'model uncertainty' – where players do not only have incomplete information about the payoff functions of the other players, but also about their own payoff function – affects the prospects of international cooperation. Using a simple game-theoretic model, it is shown how countries can use the veil of uncertainty to hide their distributional interests. The arguments are based on a deviation from the common prior assumption, which seems particularly questionable in a setting comprising various countries with different cultural and scientific backgrounds. Finally the model will prove useful to quantitatively and qualitatively illustrate the central role of model uncertainty in the negotiations of the first Sulphur Protocol signed to combat transboundary acidification.     

Fiscal and monetary interactions when wage-setters are large: is there a role for corporatist policies?

This paper studies the macroeconomic consequences of alternative policy regimes in a closed economy where a central bank, a fiscal authority and a monopoly union interact via their effects on output and inflation. The analysis compares macroeconomic outcomes in a non-cooperative setting, where players may move sequentially or simultaneously, and in a regime of cooperation between the government and wage-setters. The cooperative regime captures a climate of accord among social parties that is finalised at common macroeconomic targets in the tradition of corporatism, as in the recent experience of “social pacts” in many European countries. The paper makes two main contributions. First, it shows that macroeconomic outcomes are suboptimal in the non-cooperative regime and may deliver extreme (undesirable) results even when all players share common ideal targets for output and inflation. All players would be better off with a less extreme value for output or inflation, yet they fail to reach a more advantageous allocation as long as there is an inherent conflict among their further objectives. Moreover, the result is robust to a change in the degree of central bank’s conservatism. Second, I find that cooperation between the government and the monopoly union towards common ideal targets for inflation, output and taxes enhances social welfare even in the absence of explicit coordination with the central bank.     

An experiment on learning with limited information: nonconvergence, experimentation cascades, and the advantage of being slow

We present the results of an experiment on learning in a continuous-time low-information setting. For a dominance solvable version of a Cournot oligopoly with differentiated products, we find little evidence of convergence to the Nash equilibrium. In an asynchronous setting, characterized by players updating their strategies at different frequencies, play tends toward the Stackelberg outcome which favors the slower player. Convergence is significantly more robust for a “serial cost sharing” game, which satisfies a stronger solution concept of overwhelmed solvability. As the number of players grows, this improved convergence tends to diminish, seemingly driven by frequent and highly structured experimentation by players leading to a cascading effect in which experimentation by one player induces experimentation by others. These results have implications both for traditional oligopoly competition and for a wide variety of strategic situations arising on the Internet.