Interactive Epistemology and Solution Concepts for Games with Asymmetric Information

Battigalli, Pierpaolo; Tillio, Alfredo Di; Grillo, Edoardo; Penta, Antonio

doi:10.2139/ssrn.1494889

Cited by 19 publications

(39 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Another example is that players' beliefs about the state of nature conform to a given prior on Θ. An example of restrictions on endogenous beliefs is that players' beliefs satisfy certain independence or conditional independence properties (see Dekel et al (2007) and Battigalli et al (2007)). Furthermore, we allow for the possibility that such restrictions may depend upon each player's information type.…”

Section: Restrictions On Beliefsmentioning

confidence: 99%

Interactive epistemology in games with payoff uncertainty

Battigalli

Siniscalchi

2007

Research in Economics

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Restrictions On Beliefsmentioning

confidence: 99%

Interactive epistemology in games with payoff uncertainty

Battigalli

Siniscalchi

2007

Research in Economics

Self Cite

View full text Add to dashboard Cite

show abstract

“…8 The combination of this features yields that players hold, indeed, correct beliefs about how their opponents play, since: they hold correct beliefs about how information is distributed and they hold correct beliefs about how, specifically, choice is made contingent on information. For examples of epistemic frameworks that offer a more transparent distinction between equilibrium assumptions (as the two mentioned) and common knowledge of rationality see Tan and Werlang (1988), Dekel et al (2007) or Battigalli et al (2011).…”

Section: 'Correlated Equilibria As An Expression Of Bayesian Rationalmentioning

confidence: 99%

Bounded rationality and correlated equilibria

Germano

Zuazo-Garin

2016

Int J Game Theory

View full text Add to dashboard Cite

We study an interactive framework that explicitly allows for nonrational behavior. We do not place any restrictions on how players' behavior deviates from rationality. Instead we assume that there exists a probability p such that all players play rationally with at least probability p, and all players believe, with at least probability p, that their opponents play rationally. This, together with the assumption of a common prior, leads to what we call the set of p-rational outcomes, which we define and characterize for arbitrary probability p. We then show that this set varies continuously in p and converges to the set of correlated equilibria as p approaches 1, thus establishing robustness of the correlated equilibrium concept to relaxing rationality and common knowledge of rationality. The p-rational outcomes are easy to compute, also for games of incomplete information, and they can be applied to observed frequencies of play to derive a measure p that bounds from below the probability with which any given player chooses actions consistent with payoff maximization and common knowledge of payoff maximization.Keywords: strategic interaction, correlated equilibrium, robustness to bounded rationality, approximate knowledge, incomplete information, measure of rationality, experiments. JEL Classification: C72, D82, D83.

show abstract

“…A strategy is consistent with RCBR precisely if it is belief-free rationalizable (see Battigalli et al, 2011, and references therein). Moreover, a strategy is consistent with the restrictions on belief hierarchies about payoff types expressed by a given type space and RCBR if and only if it is interim correlated rationalizable for that type space (Dekel et al, 2007;Battigalli et al, 2011). Therefore, every strategy that is interim correlated rationalizable for some type space is also belief-free rationalizable.…”

Section: Introductionmentioning

confidence: 99%

Robust virtual implementation under common strong belief in rationality

Müller

2016

Journal of Economic Theory

View full text Add to dashboard Cite

Bergemann and Morris (2009b) show that static mechanisms cannot robustly virtually implement non-constant social choice functions if preferences are sufficiently interdependent. Without any knowledge of how agents revise their beliefs this impossibility result extends to dynamic mechanisms. In contrast, we show that if the agents revise their beliefs according to the forward-induction logic embedded in strong rationalizability, admitting dynamic mechanisms leads to considerable gains. We show that all ex-post incentive compatible social choice functions are robustly virtually implementable in private consumption environments satisfying a weak sufficient condition, regardless of the level of preference interdependence. This result derives from the key insight that in such environments, in every belief-complete type space under common strong belief in rationality (Battigalli and Siniscalchi, 2002), dynamic mechanisms can distinguish all payoff type profiles by their strategic choices. Notably, dynamic mechanisms can robustly virtually implement the efficient allocation of an object in cases that static mechanisms cannot.

show abstract

Interactive Epistemology and Solution Concepts for Games with Asymmetric Information

Cited by 19 publications

References 28 publications

Interactive epistemology in games with payoff uncertainty

Interactive epistemology in games with payoff uncertainty

Bounded rationality and correlated equilibria

Robust virtual implementation under common strong belief in rationality

Contact Info

Product

Resources

About