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Revealing Sequential Rationality and Forward Induction

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  • Pierfrancesco Guarino

Abstract

Given a dynamic ordinal game, we deem a strategy sequentially rational if there exist a Bernoulli utility function and a conditional probability system with respect to which the strategy is a maximizer. We establish a complete class theorem by characterizing sequential rationality via the new Conditional B-Dominance. Building on this notion, we introduce Iterative Conditional B-Dominance, which is an iterative elimination procedure that characterizes the implications of forward induction in the class of games under scrutiny and selects the unique backward induction outcome in dynamic ordinal games with perfect information satisfying a genericity condition. Additionally, we show that Iterative Conditional B-Dominance, as a `forward induction reasoning' solution concept, captures: $(i)$ the unique backward induction outcome obtained via sophisticated voting in binary agendas with sequential majority voting; $(ii)$ farsightedness in dynamic ordinal games derived from social environments; $(iii)$ a unique outcome in ordinal Money-Burning Games.

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  • Pierfrancesco Guarino, 2023. "Revealing Sequential Rationality and Forward Induction," Papers 2312.03536, arXiv.org.
    • Handle: RePEc:arx:papers:2312.03536
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    References listed on IDEAS

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    1. Kyle Bagwell & Garey Ramey, 1996. "Capacity, Entry, and Forward Induction," RAND Journal of Economics, The RAND Corporation, vol. 27(4), pages 660-680, Winter.
    2. Gilboa, Itzhak & Schmeidler, David, 2003. "A derivation of expected utility maximization in the context of a game," Games and Economic Behavior, Elsevier, vol. 44(1), pages 172-182, July.
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