A Semi-Potential for Finite and Infinite Games in Extensive Form

Stéphane Le Roux () and Arno Pauly ()
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Stéphane Le Roux: Université Paris-Saclay
Arno Pauly: Swansea University

Dynamic Games and Applications, 2020, vol. 10, issue 1, No 6, 120-144

Abstract: Abstract We consider a dynamic approach to games 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 sequential games the corresponding restriction of better-response dynamics will converge to a Nash equilibrium in quadratic 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 $$\Delta ^0_2$$Δ20-sets.

Keywords: Sequential games; Convergence; Belief learning; Infinite games (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13235-019-00301-7

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