Interactive epistemology in games with payoff uncertainty

Abstract

We adopt an interactive epistemology perspective to analyse dynamic games with partially unknown payoff functions. We consider solution procedures that iteratively delete strategies conditional on private information about the state of nature. In particular we focus on a weak and a strong version of the ∆-rationalizability solution concept, where ∆ represents given restrictions on players' beliefs about state of nature and strategies . Rationalizability in infinite, dynamic games of incomplete information. Research in Economics 57, 1-38; Battigalli, P., Siniscalchi, M., 2003. Rationalization and incomplete information. Advances in Theoretical Economics 3 (Article 3). http://www.bepress.com/bejte/advances/vol3/iss1/art3]. We first show that weak ∆-rationalizability is characterized by initial common certainty of rationality and of the restrictions ∆, whereas strong ∆-rationalizability is characterized by common strong belief in rationality and the restrictions ∆ (cf. [Battigalli, P., Siniscalchi, M., 2002. Strong belief and forward induction reasoning. Journal of Economic Theory 106, 356-391]). The latter result allows us to obtain an epistemic characterization of the iterated intuitive criterion. Then we use the framework to analyse the robustness of complete-information rationalizability solution concepts to the introduction of "slight" uncertainty about payoffs. If the set of conceivable payoff functions is sufficiently large, the set of strongly rationalizable strategies with slight payoff uncertainty coincides with the set of complete-information, weakly rationalizable strategies.

Interactive epistemology in simple dynamic games with a continuum of strategies

“…Comment: Structure is also called "game with payo¤ uncertainty" (Battigalli and Siniscalchi, 2007) or "basic game" (Bergemann and Morris, 2016) to distinguish it from Bayesian games (Harsanyi, 1967-68), that is, richer structures implicitly describing players' in…nite hierarchies of exogenous initial beliefs about . The epistemic structures considered in this paper implicitly describe players'in…nite hierarchies of conditional beliefs based on ( S; H), from which one can derive in…nite hierarchies of exogenous initial beliefs.…”

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We extend the epistemic analysis of dynamic games of Battigalli and Siniscalchi (1999, 2002, 2007 from …nite dynamic games to all simple games, that is, …nite and in…nite-horizon games with …nite action sets at non-terminal stages and compact action sets at terminal stages. We prove a generalization of Lubin's (1974) extension result to deal with conditional probability systems and strong belief.

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Higher Order Uncertainty and Information: Static and Dynamic Games

“…If the game is static, ISR coincides with ICR. The existing solution concept that is closest in spirit is Battigalli and Siniscalchi's (2007) weak Δ-rationalizability, which is only defined for games without a type space. 19 Penta (2010b) also showed that, in private values environments, ISR is (generically) equivalent to Dekel and Fudenberg's (1990) S ∞ W procedure applied to the interim normal form.…”

Uncertain information structures and backward induction

“…Previous literature on implications of incomplete information in extensive-form games include Battigalli and Siniscalchi (2007) and Penta (2011Penta ( , 2012 among others. However, these works focus on payoff uncertainty, meaning that a history of actions itself does not determine payoffs unless some other certain payoff-relevant parameter is also considered so that issues regarding beliefs on the information structure of the game are not covered.…”