Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Generalised weakened fictitious play
AU - Leslie, David S.
AU - Collins, E. J.
PY - 2006/8/1
Y1 - 2006/8/1
N2 - A general class of adaptive processes in games is developed, which significantly generalises weakened fictitious play [Van der Genugten, B., 2000. A weakened form of fictitious play in two-person zero-sum games. Int. Game Theory Rev. 2, 307–328] and includes several interesting fictitious-play-like processes as special cases. The general model is rigorously analysed using the best response differential inclusion, and shown to converge in games with the fictitious play property. Furthermore, a new actor–critic process is introduced, in which the only information given to a player is the reward received as a result of selecting an action—a player need not even know they are playing a game. It is shown that this results in a generalised weakened fictitious play process, and can therefore be considered as a first step towards explaining how players might learn to play Nash equilibrium strategies without having any knowledge of the game, or even that they are playing a game.
AB - A general class of adaptive processes in games is developed, which significantly generalises weakened fictitious play [Van der Genugten, B., 2000. A weakened form of fictitious play in two-person zero-sum games. Int. Game Theory Rev. 2, 307–328] and includes several interesting fictitious-play-like processes as special cases. The general model is rigorously analysed using the best response differential inclusion, and shown to converge in games with the fictitious play property. Furthermore, a new actor–critic process is introduced, in which the only information given to a player is the reward received as a result of selecting an action—a player need not even know they are playing a game. It is shown that this results in a generalised weakened fictitious play process, and can therefore be considered as a first step towards explaining how players might learn to play Nash equilibrium strategies without having any knowledge of the game, or even that they are playing a game.
KW - Fictitious play
KW - Best response differential inclusion
KW - Stochastic approximation
KW - Actor–critic process
U2 - 10.1016/j.geb.2005.08.005
DO - 10.1016/j.geb.2005.08.005
M3 - Journal article
VL - 56
SP - 285
EP - 298
JO - Games and Economic Behavior
JF - Games and Economic Behavior
SN - 0899-8256
IS - 2
ER -