2017/07/25 by Brian R. Swenson, Swenson, Brian, Soummya Kar +1
Decision Sciences · #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Mathematics #Game Theory and Applications #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1707.08055
openalex publication_date 2017/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper studies fictitious play (FP) learning dynamics in continuous time.\nIt is shown that in almost every potential game, and for almost every initial\ncondition, the rate of convergence of FP is exponential. In particular, the\npaper focuses on studying the behavior of FP in potential games in which all\nequilibria of the game are regular, as introduced by Harsanyi. Such games are\nreferred to as regular potential games. Recently it has been shown that almost\nall potential games (in the sense of the Lebesgue measure) are regular. In this\npaper it is shown that in any regular potential game (and hence, in almost\nevery potential game), FP converges to the set of Nash equilibria at an\nexponential rate from almost every initial condition.\n