Continuous fictitious play in zero-sum games (original) (raw)

Abstract

ABSTRACT Robinson (1951) showed that the learning process of Discrete Ficti-tious Play converges to Nash equilibrium in two-player zero-sum games for any initial condition. In several earlier works, Brown (1949, 1951) makes some heuristic arguments for a similar convergence result for the case of Continuous Fictitious Play (CFP). The standard reference for a formal proof is Harris (1998); his argument requires several technical lemmas, and moreover, involves the advanced machinery of Lyapunov functions. In this note we present a simple alternative proof. In particular, we show that Brown's convergence result follows easily from a result obtained by Monderer et al. (1997).

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