Rationalization and Incomplete Information

Battigalli, Pierpaolo; Siniscalchi, Marciano

doi:10.2202/1534-5963.1073

Cited by 136 publications

(202 citation statements)

References 41 publications

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“…We would like to point out that the finite valuation bound V and level bound K are needed only to ensure that our mechanism has a finite action space. We impose this restriction because our epistemic characterization in Section S4 of level-k rationality (i.e., by means of an iterated deletion procedure) only applies to finite games, similar to many other characterizations of higher-level rationality (Dekel, Fudenberg, and Morris (2007), Bergemann and Morris (2014), Brandenburger and Dekel (1987), Battigali and Siniscalchi (2003), Weinstein and Yildiz (2007), Halpern and Pass (2013)). …”

Section: Discrete Versus Continuous Valuation Spacementioning

confidence: 99%

Tight Revenue Bounds With Possibilistic Beliefs and Level-k Rationality

Chen¹,

Micali²,

Pass³

2015

Econometrica

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Mechanism design enables a social planner to obtain a desired outcome by leveraging the players' rationality and their beliefs. It is thus a fundamental, but yet unproven, intuition that the higher the level of rationality of the players, the better the set of obtainable outcomes. In this paper, we prove this fundamental intuition for players with possibilistic beliefs, a model long considered in epistemic game theory. Specifically, • We define a sequence of monotonically increasing revenue benchmarks for single‐good auctions, G0≤G1≤G2≤⋯, where each Gi is defined over the players' beliefs and G0 is the second‐highest valuation (i.e., the revenue benchmark achieved by the second‐price mechanism). • We (1) construct a single, interim individually rational, auction mechanism that, without any clue about the rationality level of the players, guarantees revenue Gk if all players have rationality levels ≥k+1, and (2) prove that no such mechanism can guarantee revenue even close to Gk when at least two players are at most level‐k rational.

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Section: Discrete Versus Continuous Valuation Spacementioning

confidence: 99%

Tight Revenue Bounds With Possibilistic Beliefs and Level-k Rationality

Chen¹,

Micali²,

Pass³

2015

Econometrica

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“…Battigalli and Siniscalchi (2003) using -rationalizability, being an iterative procedure of eliminating type-strategy pairs in which the strategy is strictly dominated according to player's beliefs or which are contradicted by a history of play.…”

Section: Appendix 3: Incomplete Distorted or Ambiguous Informationmentioning

confidence: 99%

“…There are many attempts to extend the concept of Nash equilibria to make it work in the case of incomplete information: among others, Bayesian equilibria introduced by Harsanyi (1967), correlated equilibria introduced by Aumann (1974Aumann ( , 1987, -rationalizability introduced by Battigalli and Siniscalchi (2003), self-confirming equilibria introduced by Fudenberg and Levine (1993) and subjective equilibria introduced by Lehrer (1993, 1995).…”

Section: Introductionmentioning

confidence: 99%

Belief distorted Nash equilibria: introduction of a new kind of equilibrium in dynamic games with distorted information

Wiszniewska-Matyszkiel¹

2015

Ann Oper Res

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In this paper the concept of belief distorted Nash equilibrium (BDNE) is introduced. It is a new concept of equilibrium for games in which players have incomplete, ambiguous or distorted information about the game they play, especially in a dynamic context. The distortion of information of a player concerns the fact how the other players and/or an external system changing in response to players' decisions, are going to react to his/her current decision. The concept of BDNE encompasses a broader concept of pre-BDNE, which reflects the fact that players best respond to their beliefs, and self-verification of those beliefs. The relations between BDNE and Nash or subjective equilibria are examined, as well as the existence and properties of BDNE. Examples are presented, including models of a common ecosystem, repeated Cournot oligopoly, a repeated Minority Game or local public good with congestion effect and a repeated Prisoner's Dilemma.

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“…As the solution concept, we employ interim correlated rationalizability (Battigalli and Siniscalchi (2003) and Dekel, Fudenberg, and Morris (2007)). …”

Section: Incomplete Information Games and P-dominancementioning

confidence: 99%

On the strategic impact of an event under non-common priors

Oyama

Tercieux

2012

Games and Economic Behavior

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This paper studies the impact of a small probability event on strategic behavior in incomplete information games with non-common priors. It is shown that the global impact of a small probability event (i.e., its propensity to affect strategic behavior at all states in the state space) has an upper bound that is an increasing function of a measure of discrepancy from the common prior assumption. In particular, its global impact can be arbitrarily large under non-common priors, but is bounded from above under common priors. These results quantify the different implications common prior and non-common prior models have on the (infinite) hierarchies of beliefs. Journal of Economic Literature Classification Numbers: C72, D82.

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Rationalization and Incomplete Information

Cited by 136 publications

References 41 publications

Tight Revenue Bounds With Possibilistic Beliefs and Level-k Rationality

Tight Revenue Bounds With Possibilistic Beliefs and Level-k Rationality

Belief distorted Nash equilibria: introduction of a new kind of equilibrium in dynamic games with distorted information

On the strategic impact of an event under non-common priors

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