Cooperation in Symmetric and Asymmetric Prisoner's Dilemma Games

We experimentally study the effect of asymmetry on cooperation in a 40 period prisoner's dilemma game in fixed partner design. We distinguish between a high and low payoff symmetric prisoner's dilemma and an asymmetric game combined out of both symmetric ones. Asymmetry significantly decreases cooperation, as low-type players are more likely to defect after mutual cooperation while high-type players initiate cooperation more often than the former. Asymmetry also has a significant negative effect on the stability of cooperation rendering long sequences of mutual cooperation extremely rare.Symmetry, Asymmetry, Prisoner's Dilemma, Experiments

Simulating Evolutionary Games: A Python-Based Introduction

This paper is an introduction to agent-based simulation using the Python programming language. The core objective of the paper is to enable students, teachers, and researchers immediately to begin social-science simulation projects in a general purpose programming language. This objective is facilitated by design features of the Python programming language, which we very briefly discuss. The paper has a 'tutorial' component, in that it is enablement-focused and therefore strongly application-oriented. As our illustrative application, we choose a classic agent-based simulation model: the evolutionary iterated prisoner's dilemma. We show how to simulate the iterated prisoner's dilemma with code that is simple and readable yet flexible and easily extensible. Despite the simplicity of the code, it constitutes a useful and easily extended simulation toolkit. We offer three examples of this extensibility: we explore the classic result that topology matters for evolutionary outcomes, we show how player type evolution is affected by payoff cardinality, and we show that strategy evaluation procedures can affect strategy persistence. Social science students and instructors should find that this paper provides adequate background to immediately begin their own simulation projects. Social science researchers will additionally be able to compare the simplicity, readability, and extensibility of the Python code with comparable simulations in other languages.Agent-Based Simulation, Python, Prisoner's Dilemma

General Tit-For-Tat Strategy in The Three Players Prisoner’s Dilemma Game

Tit-For-Tat Strategy which introduced by Robert Axelrod is a highly effective strategy in the iterated Prisoner’s Dilemma. Most game theory research on the prisoner's dilemma has focused on two players, but it is possible to create a Prisoner’s Dilemma involving three or even more players. In this Paper, we discuss a prisoner's dilemma game involving three players which is infinitely iterated “iterated three player Prisoner’s Dilemma game (I3PD)”. The all possible strategies which depend on the previous outcomes are represented by finite state of automata. Four different new strategies are presented in order to discuss the general Tit-For-Tat concept in details, and we the compute the all payoff values for these strategies with the strategy ALLC and the strategy ALLD

Computing Nash equilibria and evolutionarily stable states of evolutionary games

Stability analysis is an important research direction in evolutionary game theory. Evolutionarily stable states have a close relationship with Nash equilibria of repeated games, which are characterized by the folk theorem. When applying the folk theorem, one needs to compute the minimax profile of the game in order to find Nash equilibria. Computing the minimax profile is an NP-hard problem. In this paper we investigate a new methodology to compute evolutionary stable states based on the level-k equilibrium, a new refinement of Nash equilibrium in repeated games. A level-k equilibrium is implemented by a group of players who adopt reactive strategies and who have no incentive to deviate from their strategies simultaneously. Computing the level-k equilibria is tractable because the minimax payoffs and strategies are not needed. As an application, this paper develops a tractable algorithm to compute the evolutionarily stable states and the Pareto front of n-player symmetric games. Three games, including the iterated prisoner’s dilemma, are analyzed by means of the proposed methodology

Evolutionary Game Theory

Articl

Strategic interaction in the Prisoner's Dilemma: A game-theoretic dimension of conflict research

This four-part enquiry treats selected theoretical and empirical developments in the Prisoner's Dilemma. The enquiry is oriented within the sphere of game-theoretic conflict research, and addresses methodological and philosophical problems embedded in the model under consideration. In Part One, relevant taxonomic criteria of the von Neumann- Morgenstern theory of games are reviewed, and controversies associated with both the utility function and game-theoretic rationality are introduced. In Part Two, salient contributions by Rapoport and others to the Prisoner's Dilemma are enlisted to illustrate the model's conceptual richness and problematic wealth. Conflicting principles of choice, divergent concepts of rational choice, and attempted resolutions of the dilemma are evaluated in the static mode. In Part Three, empirical interaction among strategies is examined in the iterated mode. A computer-simulated tournament of competing families of strategies is conducted, as both a complement to and continuation of Axelrod's previous tournaments. Combinatoric sub-tournaments are exhaustively analyzed, and an eliminatory ecological scenario is generated. In Part Four, the performance of the maximization family of strategies is subjected to deeper analysis, which reveals critical strengths and weaknesses latent in its decision-making process. On the whole, an inter-modal continuity obtains, which suggests that the maximization of expected utility, weighted toward probabilistic co-operation, is a relatively effective strategic embodiment of Rapoport's ethic of collective rationality

Power asymmetries and punishment in a prisoner's dilemma with variable cooperative investment

In many two-player games, players that invest in punishment finish with lower payoffs than those who abstain from punishing. These results question the effectiveness of punishment at promoting cooperation, especially when retaliation is possible. It has been suggested that these findings may stem from the unrealistic assumption that all players are equal in terms of power. However, a previous empirical study which incorporated power asymmetries into an iterated prisoner's dilemma (IPD) game failed to show that power asymmetries stabilize cooperation when punishment is possible. Instead, players cooperated in response to their partner cooperating, and punishment did not yield any additional increase in tendency to cooperate. Nevertheless, this previous study only allowed an all-or-nothing–rather than a variable–cooperation investment. It is possible that power asymmetries increase the effectiveness of punishment from strong players only when players are able to vary their investment in cooperation. We tested this hypothesis using a modified IPD game which allowed players to vary their investment in cooperation in response to being punished. As in the previous study, punishment from strong players did not increase cooperation under any circumstances. Thus, in two-player games with symmetric strategy sets, punishment does not appear to increase cooperation

An Experimental Investigation of Fairness and Reciprocal Behavior in a Triangular Principal'-Multiagent Relationship.

A laboratory investigation of a simple agency model that allow to study how the principal's fairness affects the attitude towards cooperation between two interdependent agents performing a simple production task.principal-agent theory; prisoner's dilemma; reciprocity; fairness; experimental economics