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Epistemic characterizations of iterated deletion of inferior strategy profiles in preference-based type spaces

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  • Michael Trost

Abstract

Bonanno (Logics and the foundations of game and decision theory, Amsterdam University Press, Amsterdam, 2008 ) provides an epistemic characterization for the solution concept of iterated deletion of inferior strategy profiles (IDIP) by embedding strategic-form games with ordinal payoffs in non-probabilistic epistemic models which are built on Kripke frames. In this paper, we will follow the event-based approach to epistemic game theory and supplement strategic games with type space models, where each type is associated with a preference relation on the state space. In such a framework, IDIP can be characterized by the conditions that at least one player has correct beliefs about the state of the world and that there is common belief that every player is rational, has correct beliefs about the state of the world and has strictly monotone preferences. Moreover, we shall compare the epistemic motivations for IDIP and its mixed strategy variant known as strong rationalizability (SR). Presuppose the above conditions. Whenever there is also common belief that players’ preferences are representable by some expected utility function IDIP still applies. But if there is common belief that players’ preferences are representable by some expected payoff function, then SR results. Copyright Springer-Verlag 2013

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  • Michael Trost, 2013. "Epistemic characterizations of iterated deletion of inferior strategy profiles in preference-based type spaces," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 755-776, August.
    • Handle: RePEc:spr:jogath:v:42:y:2013:i:3:p:755-776
    DOI: 10.1007/s00182-011-0315-5
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    References listed on IDEAS

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    1. Bonanno, Giacomo & Tsakas, Elias, 2018. "Common belief of weak-dominance rationality in strategic-form games: A qualitative analysis," Games and Economic Behavior, Elsevier, vol. 112(C), pages 231-241.
    2. Hillas, John & Samet, Dov, 2020. "Dominance rationality: A unified approach," Games and Economic Behavior, Elsevier, vol. 119(C), pages 189-196.
    3. Giacomo Bonanno & Elias Tsakas, 2017. "Qualitative analysis of common belief of rationality in strategic-form games," Working Papers 181, University of California, Davis, Department of Economics.
    4. Giacomo Bonanno & Elias Tsakas, 2017. "Qualitative analysis of common belief of rationality in strategic-form games," Working Papers 175, University of California, Davis, Department of Economics.
    5. Hillas, John & Samet, Dov, 2022. "Non-Bayesian correlated equilibrium as an expression of non-Bayesian rationality," Games and Economic Behavior, Elsevier, vol. 135(C), pages 1-15.

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