منابع مشابه
Generalised weakened fictitious play
A general class of adaptive process in games is developed, which significantly generalises weakened fictitious play (Van der Genugten, 2000) 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 ...
متن کاملBrown's original fictitious play
What modern game theorists describe as “fictitious play” is not the learning process George W. Brown defined in his 1951 paper. His original version differs in a subtle detail, namely the order of belief updating. In this note we revive Brown’s original fictitious play process and demonstrate that this seemingly innocent detail allows for an extremely simple and intuitive proof of convergence i...
متن کاملFictitious play in coordination games
We study the Fictitious Play process with bounded and unbounded recall in pure coordination games for which failing to coordinate yields a payoff of zero for both players. It is shown that every Fictitious Play player with bounded recall may fail to coordinate against his own type. On the other hand, players with unbounded recall are shown to coordinate (almost surely) against their own type as...
متن کاملPayoff Performance of Fictitious Play
We investigate how well continuous-time fictitious play in two-player games performs in terms of average payoff, particularly compared to Nash equilibrium payoff. We show that in many games, fictitious play outperforms Nash equilibrium on average or even at all times, and moreover that any game is linearly equivalent to one in which this is the case. Conversely, we provide conditions under whic...
متن کامل.1 Discrete-time Fictitious Play
In this lecture we define several variants of the fictitious play dynamic, and study some of the properties of fictitious play. Throughout the section we consider a finite N -player game, where each player i has a finite pure action set Ai. We let ai denote a pure action for player i, and let si ∈ ∆(Ai) denote a mixed action for player i. We will typically view si as a vector in Ri , with si(ai...
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ژورنال
عنوان ژورنال: IEEE Transactions on Automatic Control
سال: 2017
ISSN: 0018-9286,1558-2523
DOI: 10.1109/tac.2017.2709548