A Model-to-model analysis of the repeated Prisoners' Dilemma: genetic algorithms vs. evolutionary dynamics

We study the properties of the well known Replicator Dynamics when applied to a finitely repeated version of the Prisoners' Dilemma game. We characterize the behavior of such dynamics under strongly simplifying assumptions (i.e. only 3 strategies are available) and show that the basin of attraction of defection shrinks as the number of repetitions increases. After discussing the difficulties involved in trying to relax the 'strongly simplifying assumptions' above, we approach the same model by means of simulations based on genetic algorithms. The resulting simulations describe a behavior of the system very close to the one predicted by the replicator dynamics without imposing any of the assumptions of the analytical model. Our main conclusion is that analytical and computational models are good complements for research in social sciences. Indeed, while on the one hand computational models are extremely useful to extend the scope of the analysis to complex scenar

Complementarities between mathematical and computational modeling: the case of the repeated Prisoners' Dilemma

We study the properties of the well known Replicator Dynamics when applied to a finitely repeated version of the Prisoners' Dilemma game. We characterize the behavior of such dynamics under strongly simplifying assumptions (i.e. only 3 strategies are available) and show that the basin of attraction of defection shrinks as the number of repetitions increases. After discussing the difficulties involved in trying to relax the 'strongly simplifying assumptions' above, we approach the same model by means of simulations based on genetic algorithms. The resulting simulations describe a behavior of the system very close to the one predicted by the replicator dynamics without imposing any of the assumptions of the mathematical model. Our main conclusion is that mathematical and computational models are good complements for research in social sciences. Indeed, while computational models are extremely useful to extend the scope of the analysis to complex scenarios hard to analyze mathematically, formal models can be useful to verify and to explain the outcomes of computational models.

A One-Shot Prisoners Dilemma with Procedural Utility

This article introduces a model of rationality that combines procedural utility over actions with consequential utility over payoffs. It applies the model to the Prisoners Dilemma and shows that empirically observed cooperative behaviors can be rationally explained by a procedural utility for cooperation. The model characterizes the situations in which cooperation emerges as a Nash equilibrium. When rational individuals are not solely concerned by the consequences of their behavior but also care for the process by which these consequences are obtained, there is no one single rational solution to a Prisoners Dilemma. Rational behavior depends on the payoffs at stake and on the procedural utility of individuals. In this manner, this model of procedural utility reflects how ethical considerations, social norms or emotions can transform a game of consequences.

A one-shot Prisoners’ Dilemma with procedural utility

This article introduces a model of rationality that combines procedural utility over actions with consequential utility over payoffs. It applies the model to the Prisoners Dilemma and shows that empirically observed cooperative behaviors can be rationally explained by a procedural utility for cooperation. The model characterizes the situations in which cooperation emerges as a Nash equilibrium. When rational individuals are not solely concerned by the consequences of their behavior but also care for the process by which these consequences are obtained, there is no one single rational solution to a Prisoners Dilemma. Rational behavior depends on the payoffs at stake and on the procedural utility of individuals. In this manner, this model of procedural utility reflects how ethical considerations, social norms or emotions can transform a game of consequences.

Effects of punishment in a mobile population playing the prisoner’s dilemma game

We deal with a system of prisoner’s dilemma players undergoing continuous motion in a two-dimensional plane. In contrast to previous work, we introduce altruistic punishment after the game. We find punishing only a few of the cooperator-defector interactions is enough to lead the system to a cooperative state in environments where otherwise defection would take over the population. This happens even with soft nonsocial punishment (where both cooperators and defectors punish other players, a behavior observed in many human populations). For high enough mobilities or temptations to defect, low rates of social punishment can no longer avoid the breakdown of cooperation

An experiment on Prisoner’s Dilemma with confirmed proposals

We suggest an alternating proposals protocol with a confirmation stage as a way of solving a Prisoner's Dilemma game. We interpret players' proposals and (no) confirmation of outcomes of the game as a tacit communication device. The protocol leads to unprecedented high levels of cooperation in the laboratory. Assigning the power of confirmation to one of the two players alone, rather than alternating the role of a leader significantly increases the probability of cooperation in the first bargaining period. We interpret pre-agreement strategies as tacit messages on players' willingness to cooperate and as signals pursuing individualistic objectives like publicizing one's bargaining abilities or eliciting those of the opponent.

Accounting for risk aversion in repeated prisoners’ dilemma games: an experimental test

We apply experimental methods to study the role of risk aversion on players’ behavior in repeated prisoners’ dilemma games. Faced with quantitatively equal discount factors, the most risk-averse players will choose Nash strategies more often in the presence of uncertainty than when future profits are discounted in a deterministic way. Overall, we find that risk aversion relates negatively with the frequency of collusive outcomes.

Working memory constrains human cooperation in the Prisoner’s Dilemma

Many problems in human society reflect the inability of selfish parties to cooperate. The “Iterated Prisoner’s Dilemma” has been used widely as a model for the evolution of cooperation in societies. Axelrod’s computer tournaments and the extensive simulations of evolution by Nowak and Sigmund and others have shown that natural selection can favor cooperative strategies in the Prisoner’s Dilemma. Rigorous empirical tests, however, lag behind the progress made by theorists. Clear predictions differ depending on the players’ capacity to remember previous rounds of the game. To test whether humans use the kind of cooperative strategies predicted, we asked students to play the iterated Prisoner’s Dilemma game either continuously or interrupted after each round by a secondary memory task (i.e., playing the game “Memory”) that constrained the students’ working-memory capacity. When playing without interruption, most students used “Pavlovian” strategies, as predicted, for greater memory capacity, and the rest used “generous tit-for-tat” strategies. The proportion of generous tit-for-tat strategies increased when games of Memory interfered with the subjects’ working memory, as predicted. Students who continued to use complex Pavlovian strategies were less successful in the Memory game, but more successful in the Prisoner’s Dilemma, which indicates a trade-off in memory capacity for the two tasks. Our results suggest that the set of strategies predicted by game theorists approximates human reality.

The prisoners' dilemma, congestion games and correlation

Social dilemmas, in particular the prisoners' dilemma, are represented as congestion games, and within this framework soft correlated equilibria as introduced by Forgó F. (2010, A generalization of correlated equilibrium: A new protocol. Mathematical Social Sciences 60:186-190) is used to improve inferior Nash payoffs that are characteristic of social dilemmas. These games can be extended to several players in different ways preserving some important characteristics of the original 2-person game. In one of the most frequently studied models of the n-person prisoners' dilemma game we measure the performance of the soft correlated equilibrium by the mediation and enforcement values. For general prisoners' dilemma games the mediation value is ∞, the enforcement value is 2. This also holds for the class of separable prisoners’ dilemma games.

An Experiment on Prisoner's Dilemma with confirmed Proposals

We apply an alternating proposals protocol with a confirmation stage as a way of solving a Prisoner’s Dilemma game. We interpret players’ proposals and (no) confirmation of outcomes of the game as a tacit communication device. The protocol leads to unprecedented high levels of cooperation in the laboratory. Assigning the power of confirmation to one of the two players alone, rather than alternating the role of a leader significantly increases the probability of signing a cooperative agreement in the first bargaining period. We interpret pre-agreement strategies as tacit messages on players’ willingness to cooperate and on their beliefs about the others’ type.

Beyond indifferent players: on the existence of prisoners dilemmas in games with amicable and adversarial preferences

Why don’t agents cooperate when they both stand to gain? This question ranks among the most fundamental in the social sciences. Explanations abound. Among the most compelling are various configurations of the prisoner’s dilemma (PD), or public goods problem. Payoffs in PD’s are specified in one of two ways: as primitive cardinal payoffs or as ordinal final utility. However, as final utility is objectively unobservable, only the primitive payoff games are ever observed. This paper explores mappings from primitive payoff to utility payoff games and demonstrates that though an observable game is a PD there are broad classes of utility functions for which there exists no associated utility PD. In particular we show that even small amounts of either altruism or enmity may disrupt the mapping from primitive payoff to utility PD. We then examine some implications of these results.

Knowledge about a species' conservation status and funding for its preservation: Analysis

Using a species’ population to measure its conservation status, this note explores how an increase in knowledge about this status would change the public’s willingness to donate funds for its conservation. This is done on the basis that the relationship between the level of donations and a species’ conservation status satisfies stated general mathematical properties. This level of donation increases, on average, with greater knowledge of a species’ conservation status if it is endangered, but falls if it is secure. Game theory and other theory is used to show how exaggerating the degree of endangerment of a species can be counterproductive for conservation.

Experimental evidence that partner choice is a driving force in the payoff distribution among cooperators or mutualists: the cleaner fish case

Supply and demand largely determine the price of goods on human markets. It has been proposed that in animals, similar forces influence the payoff distribution between trading partners in Sexual selection, intraspecific cooperation and interspecific mutualism. Here we present the first experimental evidence supporting biological market theory in it study on cleaner fish, Labroides dimidiatus. Cleaners interact with two classes of clients: choosy client species with access to several cleaners usually do not queue for service and do not return if ignored, while resident client species with access to only one cleaning station do queue or return. We used plexiglas plates with equal amounts of food to stimulate these behaviours of the two client classes. Cleaners soon inspected 'choosy' plates before 'resident' plates. This supports previous field observations that suggest that client species with access to several cleaners exert choice to receive better(immediate) service.