Unified convergence proofs of continuous-time fictitious play

Jeff S. Shamma; Gurdal Arslan

doi:10.1109/TAC.2004.831143

Unified convergence proofs of continuous-time fictitious play

Jeff S. Shamma^*, Gurdal Arslan

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

43 Scopus citations

Abstract

We consider a continuous-time version of fictitious play (FP), in which interacting players evolve their strategies in reaction to their opponents' actions without knowledge of their opponents' utilities. It is known that FP need not converge, but that convergence is possible in certain special cases including zero-sum games, identical interest games, and two-player/two-move games. We provide a unified proof of convergence in all of these cases by showing that a Lyapunov function previously introduced for zero-sum games also can establish stability in the other special cases. We go on to consider a two-player game in which only one player has two-moves and use properties of planar dynamical systems to establish convergence.

Original language	English (US)
Pages (from-to)	1137-1142
Number of pages	6
Journal	IEEE Transactions on Automatic Control
Volume	49
Issue number	7
DOIs	https://doi.org/10.1109/TAC.2004.831143
State	Published - Jul 2004
Externally published	Yes

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

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10.1109/TAC.2004.831143

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abstract = "We consider a continuous-time version of fictitious play (FP), in which interacting players evolve their strategies in reaction to their opponents' actions without knowledge of their opponents' utilities. It is known that FP need not converge, but that convergence is possible in certain special cases including zero-sum games, identical interest games, and two-player/two-move games. We provide a unified proof of convergence in all of these cases by showing that a Lyapunov function previously introduced for zero-sum games also can establish stability in the other special cases. We go on to consider a two-player game in which only one player has two-moves and use properties of planar dynamical systems to establish convergence.",

author = "Shamma, {Jeff S.} and Gurdal Arslan",

note = "Funding Information: Manuscript received October 17, 2003. Recommended by Associate Editor C. D. Charalambous. This work was supported by the Air Force Office of Scientific Research/MURI under Grant F49620-01-1-0361 and by summer support by the UF Graduate Engineering Research Center.",

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N2 - We consider a continuous-time version of fictitious play (FP), in which interacting players evolve their strategies in reaction to their opponents' actions without knowledge of their opponents' utilities. It is known that FP need not converge, but that convergence is possible in certain special cases including zero-sum games, identical interest games, and two-player/two-move games. We provide a unified proof of convergence in all of these cases by showing that a Lyapunov function previously introduced for zero-sum games also can establish stability in the other special cases. We go on to consider a two-player game in which only one player has two-moves and use properties of planar dynamical systems to establish convergence.

AB - We consider a continuous-time version of fictitious play (FP), in which interacting players evolve their strategies in reaction to their opponents' actions without knowledge of their opponents' utilities. It is known that FP need not converge, but that convergence is possible in certain special cases including zero-sum games, identical interest games, and two-player/two-move games. We provide a unified proof of convergence in all of these cases by showing that a Lyapunov function previously introduced for zero-sum games also can establish stability in the other special cases. We go on to consider a two-player game in which only one player has two-moves and use properties of planar dynamical systems to establish convergence.

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Unified convergence proofs of continuous-time fictitious play

Abstract

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