2 research outputs found
A Semi-Potential for Finite and Infinite Sequential Games (Extended Abstract)
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
Delta^0_2 sets.Comment: In Proceedings GandALF 2016, arXiv:1609.0364
A Semi-Potential for Finite and Infinite Games in Extensive Form
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 Δ02-sets