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.

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.

scholarly journals Rational Expectations in Games

2008 ◽  
Vol 98 (1) ◽  
pp. 72-86 ◽  
Author(s):  
Robert J Aumann ◽  
Jacques H Dreze
Keyword(s):  
Rational Expectations ◽  
Rational Expectation ◽  
Common Knowledge ◽  
Real Life ◽  
Common Prior ◽  
Game Situation ◽  
Life Context ◽  
Common Knowledge Of Rationality ◽  
Correlated Equilibria ◽  
Zero Sum

A player i's actions in a game are determined by her beliefs about other players; these depend on the game's real-life context, not only its formal description. Define a game situation as a game together with such beliefs; call the beliefs—and i's resulting expectation—rational if there is common knowledge of rationality and a common prior. In two-person zero-sum games, i's only rational expectation is the game's value. In an arbitrary game G, we characterize i's rational expectations in terms of the correlated equilibria of the doubled game 2G in which each of i's strategies in G appears twice. (JEL C72, D83, D84)

Game Theory and Diplomatic History

2019 ◽  
pp. 25-38
Author(s):  
Frank C. Zagare
Keyword(s):  
Game Theory ◽  
Incomplete Information ◽  
Real World ◽  
Causal Explanation ◽  
Diplomatic History ◽  
Complex Case ◽  
Theoretic Model ◽  
Perfect Bayesian Equilibrium ◽  
Bayesian Equilibrium ◽  
Game Theoretic

This chapter explores a number of issues connected with the use of game-theoretic models to organize analytic narratives. First, a causal explanation of the 1936 Rhineland crisis is developed within the confines of a game-theoretic model of asymmetric or unilateral deterrence with incomplete information. In this context, the chapter then introduces the concept of a perfect Bayesian equilibrium. Then, some methodological obstacles that may arise in a more complex case, such as the 1879 Austro-German alliance, are discussed, and suggestions for overcoming them are offered. Finally, the advantages of using game models to more fully understand real world events are highlighted.

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….”

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.

scholarly journals The anti-mercenary norm and the market for combat force

2021 ◽  
pp. 002070202199451
Author(s):  
Ulrich Petersohn
Keyword(s):  
Game Theory ◽  
Strategic Interaction ◽  
Strategic Interactions ◽  
Norm Violation ◽  
Reputational Costs

Since 2013, combat services have been increasingly exchanged on the market. This development is puzzling since the practice emerged despite an anti-mercenary norm banning such services, and without any revision of the norm. The article argues that the combat market is not a deliberate design, but the result of strategic interaction. For some, compliance with the anti-mercenary norm is the best strategy, while for others, violating the norm is best. However, once the norm violation occurs, it is in the interest of all actors to maintain a façade of compliance. Non-compliant actors benefit from the combat services, and compliant actors do not have to engage in costly sanctioning of the norm violation, and avoid the reputational costs associated with non-enforcement. The article employs game theory to investigate the strategic interactions of actors across 11 combat contracts from 2013 to 2019.

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.

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