Punishment strategies in repeated games: Evidence from experimental markets

An experiment is designed to provide a snapshot of the strategies used by players in a repeated price competition game with a random continuation rule. One hundred pairs of subjects played the game over the Internet, with subjects having a few days to make their decisions in each round. Occasionally subjects are asked to enter one-period-ahead pricing strategies instead of prices. According to the elicited strategies, between 90% and 95% of subjects punish less harshly (in their initial response to a deviation) than implied by the grim trigger strategy, and do so in a way that depends on the size of the other subjectʼs deviation. Future earnings are highest for subjects adopting the tit-for-tat strategy, even after controlling for a subjectʼs past earnings. Punishment strategies are generally softer and more graduated than implied by a grim trigger strategy, and do better as a result.     

Indirect reciprocity and strategic reputation building in an experimental helping game

We study indirect reciprocity and strategic reputation building in an experimental helping game. At any time only half of the subjects can build a reputation. This allows us to study both pure indirect reciprocity that is not contaminated by strategic reputation building and the impact of incentives for strategic reputation building on the helping rate. We find that pure indirect reciprocity exists, but also that the helping decisions are substantially affected by strategic considerations. Finally, we find that strategic do better than non-strategic players and non-reciprocal do better than reciprocal players, casting doubt on previously proposed evolutionary explanations for indirect reciprocity.     

Indirect reciprocity and strategic reputation building in an experimental helping game

We study indirect reciprocity and strategic reputation building in an experimental helping game. At any time only half of the subjects can build a reputation. This allows us to study both pure indirect reciprocity that is not contaminated by strategic reputation building and the impact of incentives for strategic reputation building on the helping rate. We find that pure indirect reciprocity exists, but also that the helping decisions are substantially affected by strategic considerations. Finally, we find that strategic do better than non-strategic players and non-reciprocal do better than reciprocal players, casting doubt on previously proposed evolutionary explanations for indirect reciprocity.     

On the value of participation: endogenous emergence of social norms in a three-player ultimatum game experiment

We report results from two different settings of a three-player ultimatum game. Under the “Monocratic” rule, a player is randomly selected to make an offer to two receivers. Under the “Democratic” rule, all three players make a proposal, and one proposal is then randomly selected. A majority vote is required to implement the proposal in either setting. Although the two rules are strategically equivalent, different patterns of behaviour emerge as the number of interactions increase. Under the “Monocratic” rule, proposers seem to be entitled to claim a larger share of the pie, and receivers are more likely to accept, than in the “Democratic” rule. We speculate that institutions allowing more participation in the process of collective choice lead to a more socially responsible behaviour in individuals.     

The effect of environmental uncertainty on the tragedy of the commons

We model a common pool resource game under environmental uncertainty, where individuals in a symmetric group face the dilemma of sharing a common resource. Each player chooses a consumption level and obtains a corresponding share of that resource, but if total consumption exceeds a sustainable level then the resource deteriorates and all players are worse-off. We consider the effect of uncertainty about the sustainable resource size on the outcome of this game. Assuming a general dynamic for resource deterioration, we study the effect of increased ambiguity (i.e., uncertain probabilities pertaining to the common resourceʼs sustainable size). We show that whereas increased risk may lead to more selfish behavior (i.e., to more consumption), increased ambiguity may have the opposite effect.     

The minority game unpacked:

We conduct an experiment on a minority-of-three game in which each player is a team composed of three subjects. Each team can freely discuss its strategies in the game and decisions must be made via majority rule. Team discussions are recorded and their content analyzed to detect evidence of strategy co-evolution among teams playing together. Our main results show no evidence supporting the mixed strategy Nash equilibrium solution, and provide evidence more consistent with reinforcement learning models than with belief-based models. Exhibiting level-2 rationality (i.e., reasoning about others’ beliefs) is positively and significantly correlated with higher than average earnings in the game. In addition, teams that are more successful tend to become more self-centered over time, paying more attention to their own past successes than to the behavior of other teams. Finally, we find evidence of mutual adaptation over time, as teams that are more strategic induce competing teams to be more self-centered instead. Our results contribute to the understanding of coordination dynamics resting on heterogeneity and co-evolution of decision rules. In addition, they provide support at the decision process level to the validity of modeling behavior using reinforcement learning models.     

Effect of an audience in public goods provision

This paper investigates a novel public goods game where contributions to the public goods require effort that is observable. When the players are observed, they exert more effort to contribute to the public goods, and free-riding diminishes significantly compared to the no observer case. These effects are absent when no effort is required in order to contribute to the public goods. Furthermore, in the presence of an audience, the contributions to the public goods do not diminish when the game is repeated in the effort-required environment. Being observed does not affect the performance of the players if there is no strategic aspect of the game, in other words, when they play a private goods game. These results indicate that an individual wants to avoid appearing lazy when her effort helps the society.     

The welfare economics of the socialization of commodities

Socialization is defined for the purpose of this paper as the acquisition by the goverment of the total output of a commodity such as medical services and redistribution of that commodity equally to all citizens. Simple general equilibrium models are constructed to show that when decisions are reached by majority rule a commodity is more likely to be socialized the greater the inequality of income in the community and the less diverse the tastes of individuals for that commodity. The interests of producers of commodities are also taken into account, and strategic aspects of voting about socialization are discussed.     

The challenge of understanding decisions in experimental studies of common pool resource governance

Common pool resource experiments in the laboratory and the field have provided insights that have contrasted to those derived from conventional non-cooperative game theory. Contrary to predictions from non-cooperative game theory, participants are sometimes willing to restrain voluntarily from over extracting resources and use costly punishment to sanction other participants. Something as simple as face-to-face communication has been shown to increase average earnings significantly. In the next generation of experiments, both in the laboratory and in the field, we need to extract more information that provides insight concerning why people make the decisions they make. More information is needed concerning attributes of individuals as well as the social and social-ecological context in which they interact that may give rise to such deviations from theoretical predictions. In the process of extracting more information from participants and the contexts in which they interact, we face several methodological and ethical challenges which we address in this paper.     

Group polarization in the team dictator game reconsidered

While most papers on team decision-making find that teams behave more selfishly, less trustingly and less altruistically than individuals, Cason and Mui (1997) report that teams are more altruistic than individuals in a dictator game. Using a within-subjects design we re-examine group polarization by letting subjects make individual as well as team decisions in an experimental dictator game. In our experiment teams are more selfish than individuals, and the most selfish team member has the strongest influence on team decisions. Various explanations for the different findings in Cason and Mui (1997) and in our paper are discussed.      

Ideology and endogenous constitutions

We study a legislature where decisions are made by playing an agenda-setting game. Legislators are concerned about their electoral prospects but they are also genuinely concerned for the legislature to make the correct decision. We show that when ideological polarization is positive but not too large (and the status quo is extremely inefficient), institutions in which the executive has either no constraints (autocracy) or many constraints (unanimity) are preferable to democracies that operate under an intermediate number of constraints (simple majority rule). When instead ideological polarization is large (and the status quo is only moderately inefficient), simple majority turns out to be preferable.     

Fault Tolerant Implementation

In this paper we investigate the implementation problem arising when some of the players are "faulty" in the sense that they fail to act optimally. The planner and the non-faulty players only know that there can be at most  k  faulty players in the population. However, they know neither the identity of the faulty players, their exact number nor how faulty players behave. We define a solution concept which requires a player to optimally respond to the non-faulty players regardless of the identity and actions of the faulty players. We introduce a notion of fault tolerant implementation, which unlike standard notions of full implementation, also requires robustness to deviations from the equilibrium. The main result of this paper establishes that under symmetric information any choice rule that satisfies two properties—  k  -monotonicity and no veto power—can be implemented by a strategic game form if there are at least three players and the number of faulty players is less than     . As an application of our result we present examples of simple mechanisms that implement the constrained Walrasian function and a choice rule for the efficient allocation of an indivisible good.     

Extensive and strategic forms: Games and models for games

This paper aims to make precise, in the context of epistemic models for games, some relations between the normal or strategic form representation of a game and the extensive or dynamic form representation. It is argued, first, that epistemic models defined for strategic form representations provide all the materials necessary for defining models for corresponding extensive form representations of the game, models that provide information about the way the game is played that is sufficient to evaluate the rationality of the choices that the players make, and are disposed to make, in the course of playing the dynamic game. Second, two definitions of rationality are compared — one for strategy choices in the normal form representation, and one for the individual choices that the player is disposed to make in the course of playing the dynamic game. It is shown that they are essentially equivalent in games with perfect recall. The main focus is on the intuitive foundational assumptions about rationality and dynamic choice that are needed to motivate the definitions. It is argued that to evaluate the rationality of a player's choices in a dynamic context, it is essential to distinguish passive knowledge (knowledge about nature and about the prior beliefs and strategy choices of other players that is based on observation and inference) fromactive knowledge (knowledge about one's own choices and future choices that is grounded in one's decisions).     

Contributing for Myself,but Free riding for My Group?

Many real‐world decisions are made by individuals as representatives of groups. Most research, however, studies either individuals or groups as decision‐makers. This paper explores whether there is a general difference between a decision made as an individual and as a representative of a group in the context of a public good game. We conducted a series of experiments to test this question and to understand mechanisms contributing to potential differences. We found that representatives contributed less than individuals when they could not communicate with their constituency. However, when they could discuss their strategy before playing, they contributed at least as much as individual decision‐makers. Furthermore, when they could justify their decision after playing, they contributed even more than individual decision‐makers. We discuss potential reasons for this and directions for future research.     

The effect of endogenous timing on coordination under asymmetric information: An experimental study

This paper investigates the role of endogenous timing of decisions on coordination under asymmetric information. In the equilibrium of a global coordination game, where players choose the timing of their decision, a player who has sufficiently high beliefs about the state of the economy undertakes an investment without delay. This decision (potentially) triggers an investment by the other player whose beliefs would have led to inaction otherwise. Endogenous timing has two distinct effects on coordination: a learning effect (early decisions reveal information) and a complementarity effect (early decisions eliminate strategic uncertainty for late movers). The experiments that we conduct to test these theoretical results show that the learning effect of timing has more impact on the subjects' behavior than the complementarity effect. We also observe that subjects' welfare improves significantly under endogenous timing.     

The evolution of sanctioning institutions: an experimental approach to the social contract

A vast amount of empirical and theoretical research on public good games indicates that the threat of punishment can curb free-riding in human groups engaged in joint enterprises. Since punishment is often costly, however, this raises an issue of second-order free-riding: indeed, the sanctioning system itself is a common good which can be exploited. Most investigations, so far, considered peer punishment: players could impose fines on those who exploited them, at a cost to themselves. Only a minority considered so-called pool punishment. In this scenario, players contribute to a punishment pool before engaging in the joint enterprise, and without knowing who the free-riders will be. Theoretical investigations (Sigmund et al., Nature 466:861–863, 2010) have shown that peer punishment is more efficient, but pool punishment more stable. Social learning, i.e., the preferential imitation of successful strategies, should lead to pool punishment if sanctions are also imposed on second-order free-riders, but to peer punishment if they are not. Here we describe an economic experiment (the Mutual Aid game) which tests this prediction. We find that pool punishment only emerges if second-order free riders are punished, but that peer punishment is more stable than expected. Basically, our experiment shows that social learning can lead to a spontaneously emerging social contract, based on a sanctioning institution to overcome the free rider problem.     

Coordination of strategic responses to security threats: Laboratory evidence

Laboratory experiments are used to evaluate the extent to which players in games can coordinate investments that diminish the probability of losses due to security breaches or terrorist attacks. In this environment, economically sensible investments may be foregone if their potential benefits are negated by failures to invest in security at other sites. The result is a coordination game with a desirable high-payoff, high-security equilibrium and an undesirable low-security equilibrium that may result if players do not expect others to invest in security. One unique feature of this coordination situation is that investment in security by one player generates a positive externality such that all other players’ expected payoffs are increased, regardless of those other players’ investment decisions. Coordination failures are pervasive in a baseline experiment with simultaneous decisions, but coordination is improved if players are allowed to move in an endogenously determined sequence. In addition, coordinated security investments are observed more often when the largest single security threat to individuals is preventable by their own decisions to invest in security. The security coordination game is a “potential game,” and the success of coordination on the more secure equilibrium is related to the notion of potential function maximization and basin of attraction.      

Do people make strategic commitments? Experimental evidence on strategic information avoidance

Game theory predicts that players make strategic commitments that may appear counter-intuitive. We conducted an experiment to see if people make a counter-intuitive but strategically optimal decision to avoid information. The experiment is based on a sequential Nash demand game in which a responding player can commit ahead of the game not to see what a proposing player demanded. Our data show that subjects do, but only after substantial time, learn to make the optimal strategic commitment. We find only weak evidence of physical timing effects.     

Dissertation abstract: Three essays on the determinants of behavior in the commons-experimental evidence from fishing communities in Colombia

This dissertation presents the results of a series of common pool experiments conducted in three regions of rural Colombia with individuals who face a social dilemma in their everyday lives that is similar to what was presented in the experiment. The research objectives are to develop an empirical characterization of how individual behavior deviates from purely self-interested Nash behavior and to further our understanding of the effects of alternative institutions to promote more conservative choices in common pool experiments.Groups of five subjects participated in a 20-period common pool resource game framed as a harvest decision from a fishery. Every group first played 10 rounds of a baseline limited access common pool resource game and then 10 additional rounds under one of five institutions: face-to-face communication, one of two external regulations, and communication combined with one of the two regulations. The two external regulations consisted of an individual harvest quota that was set at the efficient outcome, but differ with respect to the level of enforcement. A total of 420 individuals participated in the experiments, with individual earnings averaging slightly more than a day’s wages. The results are presented in three essays.The first essay, What Motivates Common Pool Resource Users?, develops and tests several models of pure Nash strategies of individuals who extract from a common pool resource when they are motivated by combinations of self-interest, altruism, reciprocity, inequity aversion or conformity. The results suggest that a model which balances self-interest with a strong preference for conformity best describes average strategies. The data are inconsistent with a model of pure self-interest, as well as models that combine self-interest with individual preferences for altruism, reciprocity and inequity aversion.The second essay, Communication and Regulation to Conserve Common Pool Resources, tests for interaction effects between formal regulations imposed on a community to conserve a local natural resource and non-binding verbal agreements to do the same. The results indicate that formal regulations and informal communication are mutually reinforcing in some instances, but this result is not robust across regions or regulations. Therefore, the hypothesis of a complementary relationship of formal and informal control of local natural resources cannot be supported in general; instead the effects are likely to be community-specific. There is some evidence to suggest that these effects are correlated with the relative importance of formal regulations versus informal community efforts in the community.The third essay, Within and Between Group Variation in Individual Strategies in Common Pools, analyzes the relative effects of groups and individuals within groups in explaining variation in individual harvest decisions for particular institutions, and uses a hierarchical linear model to examine how these sources of variation may vary across institutions. Communication serves to effectively coordinate individual strategies within groups, but these coordinated strategies vary considerably among groups. In contrast, externally-imposed regulatory schemes (as well as unregulated limited access) produce significant variation in the individual strategies within groups, but these strategies are roughly replicated across groups so that there is little between-group variation.     

Social Preferences in the Lab: A Comparison of Students and a Representative Population

We report from a lab experiment conducted with a sample of participants that is nationally representative for the adult population in Norway and two student samples (economics students and non‐economics students). The participants make choices both in a dictator game (a non‐strategic environment) and in a generalized trust game (a strategic environment). We find that the representative sample differs fundamentally from the student samples, both in the relative importance assigned to different moral motives (efficiency, equity, and reciprocity) and in the level of selfish behavior. It is also interesting to note that the gender effects observed in the student samples do not correspond to the gender effects observed in representative sample. Finally, whereas economics students behave less pro‐socially than non‐economics students, the two student groups are similar in the relative importance they assign to different moral motives.