A comment on: 'Learning, mutation, and long-run equilibria in games'

P. Rhode, Mark W Stegeman

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

In a recent article in this journal, Kandori, Mailath, and Rob (1993) (KMR) study the Darwinian dynamics of a 2x2 symmetric game, played repeatedly within a finite population. KMR first provide a useful general theorem concerning the stationary distribution of strategies under Darwinian dynamics. They then divide the analysis of the 2x2 game into three cases : dominant strategy (DS) games (e.g., prisoners' dilemma), coordination (C) games, and games with no symmetric pure strategy equilibrium ( NP) (e.g., battle of the sexes). In each case, KMR claim that, as the rate of mutation vanishes, the stationary distribution of strategies converges to a symmetric Nash equilibrium. They emphasize C games, which have two symmetric Nash equilibria, and characterize the conditions under which the distribution converges to the risk dominant equilibrium. In this note, we argue that while their formal conclusions for C games are correct, their results for DS and NP games are valid only for large populations of players. In small populations, Darwinian dynamics may produce non-Nash outcomes in these two cases.

Original languageEnglish (US)
Pages (from-to)443-449
Number of pages7
JournalEconometrica
Volume64
Issue number2
StatePublished - 1996
Externally publishedYes

Fingerprint

Long-run
Mutation
Game
learning
Stationary Distribution
Nash Equilibrium
prisoner
population development
Converge
Prisoner's Dilemma Game
Finite Population
Population Dynamics
Learning
Long-run equilibrium
Divides
Vanish
Strategy
Valid
Theorem

ASJC Scopus subject areas

  • Economics and Econometrics
  • Mathematics (miscellaneous)
  • Statistics and Probability
  • Social Sciences (miscellaneous)

Cite this

A comment on : 'Learning, mutation, and long-run equilibria in games'. / Rhode, P.; Stegeman, Mark W.

In: Econometrica, Vol. 64, No. 2, 1996, p. 443-449.

Research output: Contribution to journalArticle

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