TY - GEN
T1 - On the exponential rate of convergence of fictitious play in potential games
AU - Swenson, Brian
AU - Kar, Soummya
N1 - Publisher Copyright:
© 2017 IEEE.
PY - 2017/7/1
Y1 - 2017/7/1
N2 - The paper studies fictitious play (FP) learning dynamics in continuous time. It is shown that in almost every potential game, and for almost every initial condition, the rate of convergence of FP is exponential. In particular, the paper focuses on studying the behavior of FP in potential games in which all equilibria of the game are regular, as introduced by Harsanyi. Such games are referred to as regular potential games. Recently it has been shown that almost all potential games (in the sense of the Lebesgue measure) are regular. In this paper it is shown that in any regular potential game (and hence, in almost every potential game), FP converges to the set of Nash equilibria at an exponential rate from almost every initial condition.
AB - The paper studies fictitious play (FP) learning dynamics in continuous time. It is shown that in almost every potential game, and for almost every initial condition, the rate of convergence of FP is exponential. In particular, the paper focuses on studying the behavior of FP in potential games in which all equilibria of the game are regular, as introduced by Harsanyi. Such games are referred to as regular potential games. Recently it has been shown that almost all potential games (in the sense of the Lebesgue measure) are regular. In this paper it is shown that in any regular potential game (and hence, in almost every potential game), FP converges to the set of Nash equilibria at an exponential rate from almost every initial condition.
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U2 - 10.1109/ALLERTON.2017.8262748
DO - 10.1109/ALLERTON.2017.8262748
M3 - Conference contribution
AN - SCOPUS:85047937531
T3 - 55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017
SP - 275
EP - 279
BT - 55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017
Y2 - 3 October 2017 through 6 October 2017
ER -