Population games, stable games, and passivity

Michael J. Fox, Jeff S. Shamma

Research output: Contribution to journalArticlepeer-review

Abstract

The class of "stable games", introduced by Hofbauer and Sandholm in 2009, has the attractive property of admitting global convergence to equilibria under many evolutionary dynamics. We show that stable games can be identified as a special case of the feedback-system-theoretic notion of a "passive" dynamical system. Motivated by this observation, we develop a notion of passivity for evolutionary dynamics that complements the definition of the class of stable games. Since interconnections of passive dynamical systems exhibit stable behavior, we can make conclusions about passive evolutionary dynamics coupled with stable games. We show how established evolutionary dynamics qualify as passive dynamical systems. Moreover, we exploit the flexibility of the definition of passive dynamical systems to analyze generalizations of stable games and evolutionary dynamics that include forecasting heuristics as well as certain games with memory.

Original languageEnglish (US)
Pages (from-to)561-583
Number of pages23
JournalGames
Volume4
Issue number4
DOIs
StatePublished - Dec 2013
Externally publishedYes

Keywords

  • Evolutionary games
  • Passivity theory
  • Population games

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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