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

Author

Listed:
  • Stéphane Le Roux

    (Université Paris-Saclay)

  • Arno Pauly

    (Swansea University)

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.

Suggested Citation

  • Stéphane Le Roux & Arno Pauly, 2020. "A Semi-Potential for Finite and Infinite Games in Extensive Form," Dynamic Games and Applications, Springer, vol. 10(1), pages 120-144, March.
    • Handle: RePEc:spr:dyngam:v:10:y:2020:i:1:d:10.1007_s13235-019-00301-7
    DOI: 10.1007/s13235-019-00301-7
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    References listed on IDEAS

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