A Semi Potential for Finite and Infinite Sequential Games (Extended 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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