A Formal Analysis of the Evolution of Cooperation,

Abstract

We examine a formal model of the way a growing population selects behavior. The members of the population engage in randomly-selected binary interactions, with payoffs representing a Prisoners' Dilemma. We assume that players can recognize each other if they have met before, and adopt one of two dynamic strategies; they either play the non-cooperative strategy (G) at every move, which we denote D, or they play a tit-for-tat strategy, in which they begin by playing the cooperative move(C) and continue playing C if the opponent's last move was C and G if the opponent's last move was G. This latter strategy is denoted T. The interactions are repeated, and two players meet again with probability delta epsilon (0,1). Formally, it is as if each player met a random member of the population and played a discounted supergame with discount factor delta forever afterwards. We assume that the population and the mix of behaviors changes over time in a simple fashion. These qualitative dynamics will allow us to say something about the stability of various regimes of behavior in terms of population size and behavior. The organization of the paper is as follows. Section II contains the model and definitions, and examines the evolution of cooperative behavior for the special case of a static population. Section III combines the dynamics of behavior with those of population growth. Finally, Section IV relates the present results to results of repeated play where players are rational.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1984
Accession Number
ADA152539

Entities

People

  • J. A. K. Cave

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Cooperation
  • Corporations
  • Diagrams
  • Dynamics
  • Elimination
  • Equations
  • Extinction
  • Mutations
  • New York
  • Personal Information Managers
  • Phase
  • Phase Diagrams
  • Probability
  • Recognition
  • Symmetric Games
  • Trajectories

Fields of Study

  • Biology
  • Mathematics

Readers

  • Artificial Intelligence
  • Game Theory.
  • Strategic Security Studies