A dynamic analysis of the repeated prisoner's dilemma game
type: Item
instance of: scholarly article
title: A dynamic analysis of the repeated prisoner's dilemma game
zbMATH Open document ID: 0589.90096
DOI: 10.1007/BF01770977
published in: International Journal of Game Theory
publication date: 1986-01-01T00:00:00Z
review text: Inspired by Smale's analysis of the repeated prisoner's dilemma game, this paper studies a quite different approach to a dynamic description of the evolution of the repeated game. Assuming an infinite number of potential players the dynamics is defined by changes in the distribution of players over strategies, and a continuous dynamical system, describing the evolution of the distribution over strategies is obtained. Basic questions such as existence of solutions, ''good'' strategies leading to ''good'' solutions, and the stability of solutions are given exact affirmative answers. Further we obtain the results to be structurally stable. That is, small perturbations of the basic payoff matrix in the one shot game do not change the qualitative picture of the evolution. The obtained results give one possible explanation of how the basically non-cooperative behaviour of the players may lead to a cooperative outcome of the repeated game. Finally an example illustrates the applicability of the results to a duopoly model.
Mathematics Subject Classification ID: 91A20
Mathematics Subject Classification ID: 91B24
zbMATH DE Number: 3948037
zbMATH Keywords: repeated prisoner's dilemma
zbMATH Keywords: dynamic description
zbMATH Keywords: repeated game
zbMATH Keywords: infinite number of potential players
zbMATH Keywords: continuous dynamical system
zbMATH Keywords: evolution of the distribution over strategies
zbMATH Keywords: existence of solutions
zbMATH Keywords: stability of solutions
zbMATH Keywords: duopoly
author: Michael C. Blad
MaRDI profile type: Publication
cites work: Q4067388
cites work: The Logic of Animal Conflict
cites work: Sequences of Games with Varying Opponents
cites work: The Prisoner's Dilemma and Dynamical Systems Associated to Non-Cooperative Games
cites work: Evolutionarily stable strategies and game dynamics
cites work: Q3895292
description: scientific article; zbMATH DE number 3948037