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Acyclicity of improvements in finite game forms

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  • Nikolai Kukushkin

Abstract

Game forms are studied where the acyclicity, in a stronger or weaker sense, of (coalition or individual) improvements is ensured in all derivative games. In every game form generated by an ``ordered voting'' procedure, individual improvements converge to Nash equilibria if the players restrict themselves to ``minimal'' strategy changes. A complete description of game forms where all coalition improvement paths lead to strong equilibria is obtained: they are either dictatorial, or voting (or rather lobbing) about two outcomes. The restriction to minimal strategy changes ensures the convergence of coalition improvements to strong equilibria in every game form generated by a ``voting by veto'' procedure.
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  • Nikolai Kukushkin, 2011. "Acyclicity of improvements in finite game forms," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(1), pages 147-177, February.
    • Handle: RePEc:spr:jogath:v:40:y:2011:i:1:p:147-177
    DOI: 10.1007/s00182-010-0231-0
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    1. Endre Boros & Ondřej Čepek & Vladimir Gurvich & Kazuhisa Makino, 2024. "Recognizing distributed approval voting forms and correspondences," Annals of Operations Research, Springer, vol. 336(3), pages 2091-2110, May.
    2. 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.
    3. Novikova, Natalia M. & Pospelova, Irina I., 2017. "A lemma in open sequential voting by veto," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 141-144.
    4. Lihi Dery & Svetlana Obraztsova & Zinovi Rabinovich & Meir Kalech, 2019. "Lie on the Fly: Strategic Voting in an Iterative Preference Elicitation Process," Group Decision and Negotiation, Springer, vol. 28(6), pages 1077-1107, December.

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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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