Non-algebraic Convergence Proofs for Continuous-Time Fictitious Play
نویسندگان
چکیده
منابع مشابه
On the Convergence of Fictitious Play
We study the continuous time Brown-Robinson ctitious play process for non-zero sum games. We show that, in general, ctitious play cannot converge cyclically to a mixed strategy equilibrium in which both players use more than two pure strategies.
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Continuous action space games form a natural extension to normal form games with finite action sets. However, whilst learning dynamics in normal form games are now well studied, it is not until recently that their continuous action space counterparts have been examined. We extend stochastic fictitious play to the continuous action space framework. In normal form games the limiting behaviour of ...
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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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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 ...
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ژورنال
عنوان ژورنال: Dynamic Games and Applications
سال: 2011
ISSN: 2153-0785,2153-0793
DOI: 10.1007/s13235-011-0033-4