4. Rationalizability and Common Knowledge of Rationality

2014 ◽  
pp. 86-105
Keyword(s):  
Common Knowledge ◽  
Common Knowledge Of Rationality

Interpreting Knowledge in the Backward Induction Problem

Episteme ◽  
2011 ◽  
Vol 8 (3) ◽  
pp. 248-261 ◽  
Author(s):  
Ken Binmore
Keyword(s):  
Common Knowledge ◽  
Perfect Information ◽  
Backward Induction ◽  
Finite Games ◽  
Common Knowledge Of Rationality

AbstractRobert Aumann argues that common knowledge of rationality implies backward induction in finite games of perfect information. I have argued that it does not. A literature now exists in which various formal arguments are offered in support of both positions. This paper argues that Aumann's claim can be justified if knowledge is suitably reinterpreted.

scholarly journals Counterfactual Reasoning and Common Knowledge of Rationality in Normal Form Games

2004 ◽  
Vol 4 (1) ◽  
Author(s):  
Eduardo Zambrano
Keyword(s):  
Nash Equilibrium ◽  
Normal Form ◽  
Actual World ◽  
Common Knowledge ◽  
Counterfactual Reasoning ◽  
Philosophical Literature ◽  
Normal Form Games ◽  
Normal Form Game ◽  
The World ◽  
Common Knowledge Of Rationality

When evaluating the rationality of a player in a game one has to examine counterfactuals such as "what would happen if the player were to do what he does not do?" In this paper I develop a model of a normal form game where counterfactuals of this sort are evaluated as in the philosophical literature (cf. Lewis, 1973; Stalnaker, 1968). According to this method one evaluates a statement like ``what would the player believe if he were to do what he does not do'' at the world that is closest to the actual world where the hypothetical deviation occurs. I show that in this model common knowledge of rationality need not lead to rationalizability. I also present assumptions that allow rationalizability to follow from common knowledge of rationality. These assumptions suggest that rationalizability may not rely on weaker assumptions about belief consistency than Nash equilibrium.

The Logical Antinomies of Knowledge

2014 ◽  
Author(s):  
Herbert Gintis
Keyword(s):  
Nash Equilibrium ◽  
Social Behavior ◽  
Modal Logic ◽  
Common Knowledge ◽  
Correlated Equilibrium ◽  
Actual Cost ◽  
Equilibrium Concept ◽  
Logic Of Knowledge ◽  
Common Knowledge Of Rationality ◽  
The Common

The critique of common knowledge of rationality (CKR) developed in the preceding chapters should convince researchers interested in explaining social reality to simply avoid the concept. The actual cost of abandoning CKR in terms of explaining social behavior is minimal because the Nash equilibrium concept itself is problematic when the recursive nature of interagent beliefs is important and the correlated equilibrium is by far the more cogent equilibrium concept. Nevertheless, it may seem curious that we must reject CKR even in situations where all players are in fact rational. What, after all, is the problem with assuming agents know something that is in fact true? This chapter discusses the pitfalls of naïve epistemic logic, the common knowledge of logicality paradox, the Surprise Examination problem, the modal logic of knowledge, and a solution to the Surprise Examination conundrum.

Rationalizability and Common Knowledge of Rationality

2014 ◽  
Author(s):  
Herbert Gintis
Keyword(s):  
Game Theory ◽  
Normal Form ◽  
Common Knowledge ◽  
Analytical Framework ◽  
Epistemic Game Theory ◽  
Dominated Strategies ◽  
Common Knowledge Of Rationality ◽  
The Common ◽  
Rational Players ◽  
Rationality Assumption

This chapter deals with the implications of rationality in normal form games. It first explores the ramifications of the rationalizability assumption and shows that in many cases rational individuals will not play rationalizable strategies. It argues that the informal reasoning supporting rationalizability must be replaced by a more rigorous analytical framework. This framework is known as epistemic game theory. Using epistemic game theory, it presents the argument that not rationality, but rather common knowledge of rationality, implies that players will only use rationalizable strategies. The chapter concludes by showing that there is no justification of the common knowledge of rationality assumption, and hence there is no reason to believe that in general rational players will choose rationalizable strategies. It strengthens this conclusion by showing that even assuming common knowledge of rationality, there is no reason for a rational player to conform to the iterated elimination of strongly dominated strategies.

Knowledge, Awareness and Probabilistic Beliefs

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Tomasz Sadzik
Keyword(s):  
Game Theory ◽  
Incomplete Information ◽  
Common Knowledge ◽  
Strategic Interaction ◽  
Bayesian Game ◽  
Bayesian Equilibrium ◽  
Common Prior ◽  
Probabilistic Beliefs ◽  
Common Knowledge Of Rationality ◽  
Axiom Systems

Abstract Bayesian game theory investigates strategic interaction of players with full awareness but incomplete information about their environment. We extend the analysis to players with incomplete awareness, who might not be able to reason about all contingencies in the first place. We develop three logical systems for knowledge, probabilistic beliefs and awareness, and characterize their axiom systems. Bayesian equilibrium is extended to games with incomplete awareness and we show that it is consistent with common prior and speculative trade, when common knowledge of rationality is violated.

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