A semi-potential for finite and infinite sequential games

Stéphane Le Roux; Arno Pauly

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arXiv · 1309.2798

A semi-potential for finite and infinite sequential games

Stéphane Le Roux·Arno Pauly

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Abstract

We consider a dynamical approach to game in extensive forms. By restricting the convertibility relation over strategy profiles, we obtain a semi-potential (in the sense of Kukushkin), and we show that in finite games the corresponding restriction of better-response dynamics will converge to a Nash equilibrium in quadratic (finite) time. Convergence happens on a per-player basis, and even in the presence of players with cyclic preferences, the players with acyclic preferences will stabilize. Thus, we obtain a candidate notion for rationality in the presence of irrational agents. Moreover, the restriction of convertibility can be justified by a conservative updating of beliefs about the other players strategies. For infinite games in extensive form we can retain convergence to a Nash equilibrium (in some sense), if the preferences are given by continuous payoff functions; or obtain a transfinite convergence if the outcome sets of the game are $\Delta^0_2$-sets.

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BibTeX RIS

Stéphane Le Roux, Arno Pauly. 2013-09-11. A semi-potential for finite and infinite sequential games. https://arxiv.org/abs/1309.2798

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