Stochastic Darwinian equilibria in small and large populations

Mark Stegeman, Paul Rhode

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We establish necessary and sufficient conditions for the stability of stochastic Darwinian dynamics in quadratic games. Each player's strategy adjusts through mutation and selection shocks, and stability is independent of the rates at which these shocks arrive. Given stability, we characterize the midpoint of the nondegenerate ergodic distribution. In small populations, some equilibria correspond to relative payoff maximization, but others are unanticipated by existing static concepts. In the large population limit of a finite population, the set of stable Nash equilibria strictly includes all equilibria stable under myopic best reply, but some strict Nash equilibria are highly unstable. The stability result shows, for the first time, that large finite populations converge to Nash play even if they do not understand the game and strategies are so numerous that most are never played. The large population stability condition is related to risk dominance and, separately, to the static CSS condition.

Original languageEnglish (US)
Pages (from-to)171-214
Number of pages44
JournalGames and Economic Behavior
Issue number1
StatePublished - Oct 2004

ASJC Scopus subject areas

  • Finance
  • Economics and Econometrics


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