A Feedback Stabilization Approach to Fictitious Play

Jeff S. Shamma*, Gurdal Arslan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We consider repeated matrix games in which player strategies evolve in reaction to opponent actions. Players observe each other's actions, but do not have access to other player utilities. Strategy evolution may be of the best response sort, as in fictitious play, or a gradient update. Such mechanisms are known to not necessarily converge. We show that the use of derivative action in processing opponent actions can lead to behavior converging to Nash equilibria. We analyze the use of approximate differentiators and reveal a potentially detrimental biasing effect. We go on to provide alternative mechanisms to diminish or eliminate this effect. We discuss two player games throughout and outline extensions to multiplayer games. We also provide convergent simulations throughout to standard counterexamples in the literature.

Original languageEnglish (US)
Pages (from-to)4140-4145
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Volume4
StatePublished - 2003
Externally publishedYes

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Safety, Risk, Reliability and Quality
  • Chemical Health and Safety

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