par Le Roux, Stephane 
;Pauly, Arno
Référence Electronic proceedings in theoretical computer science, 226, page (242-256)
Publication Publié, 2016-09
;Pauly, Arno Référence Electronic proceedings in theoretical computer science, 226, page (242-256)
Publication Publié, 2016-09
Article révisé par les pairs
| Résumé : | We consider a dynamical approach to sequential games. 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 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 sequential games 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 Δ2 0-sets. |
