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.

Extensive Form Rationalizability

2014 ◽  
Author(s):  
Herbert Gintis
Keyword(s):  
Normal Form ◽  
Nash Equilibria ◽  
Common Knowledge ◽  
Backward Induction ◽  
Forward Induction ◽  
Extensive Form ◽  
Extensive Form Games ◽  
Dominated Strategies ◽  
Extensive Form Game ◽  
Common Knowledge Of Rationality

The extensive form of a game is informationally richer than the normal form since players gather information that allows them to update their subjective priors as the game progresses. For this reason, the study of rationalizability in extensive form games is more complex than the corresponding study in normal form games. There are two ways to use the added information to eliminate strategies that would not be chosen by a rational agent: backward induction and forward induction. The latter is relatively exotic (although more defensible). Backward induction, by far the most popular technique, employs the iterated elimination of weakly dominated strategies, arriving at the subgame perfect Nash equilibria—the equilibria that remain Nash equilibria in all subgames. An extensive form game is considered generic if it has a unique subgame perfect Nash equilibrium. This chapter develops the tools of modal logic and presents Robert Aumann's famous proof that common knowledge of rationality (CKR) implies backward induction. It concludes that Aumann is perfectly correct, and the real culprit is CKR itself. CKR is in fact self-contradictory when applied to extensive form games.

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.

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.

Book Reviews

2011 ◽  
Vol 49 (1) ◽  
pp. 133-136
Keyword(s):  
Game Theory ◽  
Decision Theory ◽  
Human Behavior ◽  
Common Knowledge ◽  
Behavioral Sciences ◽  
Key Concepts ◽  
Common Knowledge Of Rationality ◽  
Basic Concepts ◽  
Simon Fraser University

Arthur J. Robson of Simon Fraser University reviews “The Bounds of Reason: Game Theory and the Unification of the Behavioral Sciences” by Herbert Gintis. The EconLit Abstract of the reviewed work begins, “Explores how key concepts from the behavioral sciences can complement game theory in providing insights into human behavior. Discusses decision theory and human behavior; game theory--basic concepts; game theory and human behavior; rationalizability and common knowledge of rationality; extensive for….”

El patriacado y la estructura social de la vida cotidiana

1970 ◽  
Author(s):  
Marta Postigo Asenjo
Keyword(s):  
Labor Market ◽  
Public Sphere ◽  
Civic Education ◽  
Common Knowledge ◽  
Judicial System ◽  
The Public ◽  
El Sistema ◽  
The Common ◽  
The Public Sphere ◽  
Ways Of Life

RESUMENEl sistema patriarcal no afecta exclusivamente al poder político y judicial, sino que afecta a la estructura interna de la sociedad, la identidad y las formas de vida de los individuos que en ella viven. Para comprender mejor como condiciona el sistema patriarcal las formas de vida y la visión que tienen los individuos de la realidad social, hemos de analizar el modo en que se extiende al orden institucional y lo determina mediante "tipificaciones" de hechos y de personas y mediante roles concretos, esteoreotipaciones sexiuales que obstaculizan el acceso a la esfera pública de la mujer, así como su reinserción en el mercado laboral, en suma, todo aquello que afecta al conocimiento común que comparten los miembros de una comunidad. El cambio hacia una mayor igualdad y una real democracia paritaria y compartida no es posible sin una paulatina educación y concienciación de la sociedad en su conjunto.PALABRAS CLAVEPATRIARCADO-TIPIFICACIÓN SOCIAL-IGUALDAD DE GÉNEROABSTRACTPatriarchalism is not only present in politics and the judicial system. It also affects the internal structure of society, above all the life and identitý of individuals. To understand better how it conditions their ways of life and the vision the individuals have of social reality, we should study how patriarchalism r3eaches the system of institutions and how this becomes determined by "typifications" of facts and people, and by certain roles or sexual stereotypes that hinder the access of women both to the public sphere and to tha labor market. It sum, everything that concerns the common knowledge that the members of a community share. The move towards more equality and towards a more egalitarian democracy heavily depends on the spread of civic education to the entire society.KEYWORDSPATRIARCHALISM-SOCIAL TYPIFICATION-GENDER EQUALITY

scholarly journals Game Theory Without Partitions, and Applications to Speculation and Consensus

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
John Geanakoplos
Keyword(s):  
Game Theory ◽  
Information Processing ◽  
Decision Theory ◽  
Common Knowledge ◽  
Extended Theory ◽  
Knowing That ◽  
Processing Errors ◽  
Necessary And Sufficient

Abstract Decision theory and game theory are extended to allow for information processing errors. This extended theory is then used to reexamine market speculation and consensus, both when all actions (opinions) are common knowledge and when they may not be. Five axioms of information processing are shown to be especially important to speculation and consensus. They are called nondelusion, knowing that you know (KTYK), nested, balanced, and positively balanced. We show that it is necessary and sufficient that each agent's information processing errors be (1) nondeluded and balanced so that the agents cannot agree to disagree, (2) nondeluded and positively balanced so that it cannot be common knowledge that they are speculating, and (3) nondeluded and KTYK and nested so that agents cannot speculate in equilibrium. Each condition is strictly weaker than the next one, and the last is strictly weaker than partition information.

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.

INTERPERSONAL COORDINATION AND EPISTEMIC SUPPORT FOR INTENTIONS WITH WE-CONTENT

2010 ◽  
Vol 26 (3) ◽  
pp. 345-367 ◽  
Author(s):  
Olivier Roy
Keyword(s):  
Game Theory ◽  
Epistemic Logic ◽  
The Other ◽  
Interpersonal Coordination ◽  
Epistemic Game Theory ◽  
Cast Doubt ◽  
Alternative Set

In this paper I study intentions of the form ‘I intend that we . . .’, that is, intentions with a we-content, and their role in interpersonal coordination. I focus on the notion of epistemic support for such intentions. Using tools from epistemic game theory and epistemic logic, I cast doubt on whether such support guarantees the other agents' conditional mediation in the achievement of such intentions, something that appears important if intentions with a we-content are to count as genuine intentions. I then formulate a stronger version of epistemic support, one that does indeed ensure the required mediation, but I then argue that it rests on excessively strong informational conditions. In view of this I provide an alternative set of conditions that are jointly sufficient for coordination in games, and I argue that these conditions constitute a plausible alternative to the proposed notion of epistemic support.

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