Stéphane Le Roux (Universite libre de Bruxelles) |
Arno Pauly (Universite libre de Bruxelles) |

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. |

Published: 13th September 2016.

ArXived at: http://dx.doi.org/10.4204/EPTCS.226.17 | bibtex | |

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