The Evolutionary Stability of Cooperation

Summary of: The Evolutionary Stability of Cooperation

Author(s) / Editor(s)

Given a variety of strategies ranging from cooperative to combative, cooperative retaliatory strategies tend to be the most stable but remain vulnerable to invasion.

Publication Reference

Published in/by
June 1997


  • All strategies in iterative prisoner's dilemma games are vulnerable to invasion and therefore inherently unstable.
  • Tit-for-Tat (cooperative) strategies are the most stable. These strategies can withstand higher levels of invasion by competing strategies.
  • All strategies have a threshold of stability, if a certain percentage of the population adopts these strategies they can be self-maintaining.

Theorists have posited that pure tit-for-tat strategies in iterative prisoners dilemma games were invulnerable. Is this correct? The authors seek to answer this question by examining the ability of various prisoners dilemma gaming strategies to withstand invasion by other competing strategies.

Bender and Swistak examine a gaming strategy universe that includes the strategies:

  • Tit for tat - a player will initially cooperate and then in future rounds mimic the behavior of their opponent.
  • Tit for 2 Tats - a player will cooperate for the first two rounds and then defect in rounds where their opponent defected in the previous two.
  • Suspicious Tit for Tat - a player will initially defect and then will mimic their opponent in future rounds.
  • Always Defect
  • Always Cooperate
  • Grim Trigger - Begin by cooperating, if opponent defects then always defect afterward.

These strategies were examined in pure conditions where only one existed, and then competing strategies were introduced. If a given strategy could withstand incursions by competing strategies it was deemed "stable".

Stability proved to be a continuum. All strategies proved to have points of equilibrium. At this point, a strategy can withstand its maximum level of incursion. That point is that strategy's maximum stability.