Renegotiation Proofness and Climate Agreements: Some Experimental Evidence

The notion of renegotiation-proof equilibrium has become a cornerstone in non-cooperative models of international environmental agreements. Applying this solution concept to the infinitely repeated N-person Prisoners' Dilemma generates predictions that contradict intuition as well as conventional wisdom about public goods provision. This paper reports the results of an experiment designed to test two such predictions. The first is that the higher the cost of making a contribution, the more cooperation will materialize. The second is that the number of cooperators is independent of group size. Although the experiment was designed to replicate the assumptions of the model closely, our results lend very little support to the two predictions.

Predicting Human Cooperation

The Prisoner's Dilemma has been a subject of extensive research due to its importance in understanding the ever-present tension between individual self-interest and social benefit. A strictly dominant strategy in a Prisoner's Dilemma (defection), when played by both players, is mutually harmful. Repetition of the Prisoner's Dilemma can give rise to cooperation as an equilibrium, but defection is as well, and this ambiguity is difficult to resolve. The numerous behavioral experiments investigating the Prisoner's Dilemma highlight that players often cooperate, but the level of cooperation varies significantly with the specifics of the experimental predicament. We present the first computational model of human behavior in repeated Prisoner's Dilemma games that unifies the diversity of experimental observations in a systematic and quantitatively reliable manner. Our model relies on data we integrated from many experiments, comprising 168,386 individual decisions. The computational model is composed of two pieces: the first predicts the first-period action using solely the structural game parameters, while the second predicts dynamic actions using both game parameters and history of play. Our model is extremely successful not merely at fitting the data, but in predicting behavior at multiple scales in experimental designs not used for calibration, using only information about the game structure. We demonstrate the power of our approach through a simulation analysis revealing how to best promote human cooperation.Comment: Added references. New inline citation style. Added small portions of text. Re-compiled Rmarkdown file with updated ggplot2 so small aesthetic changes to plot

Co-operation in the finitely repeated prisoner’s dilemma

More than half a century after the first experiment on the finitely repeated prisoner’s dilemma, evidence on whether cooperation decreases with experience–as suggested by backward induction–remains inconclusive. This paper provides a meta-analysis of prior experimental research and reports the results of a new experiment to elucidate how cooperation varies with the environment in this canonical game. We describe forces that affect initial play (formation of cooperation) and unraveling (breakdown of cooperation). First, contrary to the backward induction prediction, the parameters of the repeated game have a significant effect on initial cooperation. We identify how these parameters impact the value of cooperation–as captured by the size of the basin of attraction of Always Defect–to account for an important part of this effect. Second, despite these initial differences, the evolution of behavior is consistent with the unraveling logic of backward induction for all parameter combinations. Importantly, despite the seemingly contradictory results across studies, this paper establishes a systematic pattern of behavior: subjects converge to use threshold strategies that conditionally cooperate until a threshold round; and conditional on establishing cooperation, the first defection round moves earlier with experience. Simulation results generated from a learning model estimated at the subject level provide insights into the long-term dynamics and the forces that slow down the unraveling of cooperation

Zero-determinant strategies in finitely repeated games

Direct reciprocity is a mechanism for sustaining mutual cooperation in repeated social dilemma games, where a player would keep cooperation to avoid being retaliated by a co-player in the future. So-called zero-determinant (ZD) strategies enable a player to unilaterally set a linear relationship between the player's own payoff and the co-player's payoff regardless of the strategy of the co-player. In the present study, we analytically study zero-determinant strategies in finitely repeated (two-person) prisoner's dilemma games with a general payoff matrix. Our results are as follows. First, we present the forms of solutions that extend the known results for infinitely repeated games (with a discount factor w of unity) to the case of finitely repeated games (0 < w < 1). Second, for the three most prominent ZD strategies, the equalizers, extortioners, and generous strategies, we derive the threshold value of w above which the ZD strategies exist. Third, we show that the only strategies that enforce a linear relationship between the two players' payoffs are either the ZD strategies or unconditional strategies, where the latter independently cooperates with a fixed probability in each round of the game, proving a conjecture previously made for infinitely repeated games.Comment: 24 pages, 2 figure

Unbeatable Imitation

We show that for many classes of symmetric two-player games, the simple decision rule "imitate-the-best" can hardly be beaten by any other decision rule. We provide necessary and sufficient conditions for imitation to be unbeatable and show that it can only be beaten by much in games that are of the rock-scissors-paper variety. Thus, in many interesting examples, like 2x2 games, Cournot duopoly, price competition, rent seeking, public goods games, common pool resource games, minimum effort coordination games, arms race, search, bargaining, etc., imitation cannot be beaten by much even by a very clever opponent

Cooperation Enforcement and Collusion Resistance in Repeated Public Goods Games

Enforcing cooperation among substantial agents is one of the main objectives for multi-agent systems. However, due to the existence of inherent social dilemmas in many scenarios, the free-rider problem may arise during agents' long-run interactions and things become even severer when self-interested agents work in collusion with each other to get extra benefits. It is commonly accepted that in such social dilemmas, there exists no simple strategy for an agent whereby she can simultaneously manipulate on the utility of each of her opponents and further promote mutual cooperation among all agents. Here, we show that such strategies do exist. Under the conventional repeated public goods game, we novelly identify them and find that, when confronted with such strategies, a single opponent can maximize his utility only via global cooperation and any colluding alliance cannot get the upper hand. Since a full cooperation is individually optimal for any single opponent, a stable cooperation among all players can be achieved. Moreover, we experimentally show that these strategies can still promote cooperation even when the opponents are both self-learning and collusive

Cooperation among strangers: an experiment with indefinite interaction

We study the emergence of norms of cooperation in experimental economies populated by strangers interacting indefinitely and lacking formal enforcement institutions. In all treatments the efficient outcome is sustainable as an equilibrium. We address the following questions: can these economies achieve full efficiency? Which institutions for monitoring and enforcement promote cooperation? Finally, what classes of strategies are employed to achieve high efficiency? We find that, first, cooperation can be sustained even in anonymous settings; second, some type of monitoring and punishment institutions significantly promote cooperation; and, third, subjects dislike indiscriminate strategies and prefer selective strategies.experiments, repeated games, cooperation, equilibrium selection, prisoners’ dilemma, random matching

Automata, matching and foraging behavior of bees

Environment;Mathematics