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Epistemic Conditions for Nash Equilibrium

Aumann, Robert; Brandenburger, Adam - In: The Language of Game Theory:Putting Epistemics into the …

Sufficient conditions for Nash equilibrium in an n-person game are given in terms of what the players know and believe — about the game, and about each other's rationality, actions, knowledge, and beliefs. Mixed strategies are treated not as conscious randomizations, but as conjectures, on the...

Persistent link: https://www.econbiz.de/10011206381

Admissibility in Games

Brandenburger, Adam; Friedenberg, Amanda; Keisler, H. Jerome - In: The Language of Game Theory:Putting Epistemics into the …

Suppose that each player in a game is rational, each player thinks the other players are rational, and so on. Also, suppose that rationality is taken to incorporate an admissibility requirement — that is, the avoidance of weakly dominated strategies. Which strategies can be played? We provide...

Persistent link: https://www.econbiz.de/10011206393

Hierarchies of Beliefs and Common Knowledge

Brandenburger, Adam; Dekel, Eddie - In: The Language of Game Theory:Putting Epistemics into the …

Game-theoretic analysis often leads to consideration of an infinite hierarchy of beliefs for each player. Harsanyi suggested that such a hierarchy of beliefs could be summarized in a single entity, called the player's type. This chapter provides an elementary construction, complementary to the...

Persistent link: https://www.econbiz.de/10011206453

Self-Admissible Sets

Brandenburger, Adam; Friedenberg, Amanda - In: The Language of Game Theory:Putting Epistemics into the …

Best-response sets (Pearce [1984]) characterize the epistemic condition of “rationality and common belief of rationality.” When rationality incorporates a weak-dominance (admissibility) requirement, the self-admissible set (SAS) concept (Brandenburger, Friedenberg, and Keisler [2008])...

Persistent link: https://www.econbiz.de/10011206587

Lexicographic Probabilities and Choice Under Uncertainty

Blume, Lawrence; Brandenburger, Adam; Dekel, Eddie - In: The Language of Game Theory:Putting Epistemics into the …

Two properties of preferences and representations for choice under uncertainty which play an important role in decision … well defined conditional probabilities, that is, given any event a conditional probability which is concentrated on that … event and which corresponds to the individual's preferences. The conventional Bayesian theory of choice under uncertainty …

Persistent link: https://www.econbiz.de/10011206642

Rationalizability and Correlated Equilibria

Brandenburger, Adam; Dekel, Eddie - In: The Language of Game Theory:Putting Epistemics into the …

We discuss the unity between the two standard approaches to noncooperative solution concepts for games. The decision-theoretic approach starts from the assumption that the rationality of the players is common knowledge. This leads to the notion of correlated rationalizability. It is shown that...

Persistent link: https://www.econbiz.de/10011206697

Intrinsic Correlation in Games

Brandenburger, Adam; Friedenberg, Amanda - In: The Language of Game Theory:Putting Epistemics into the …

Correlations arise naturally in noncooperative games, e.g., in the equivalence between undominated and optimal strategies in games with more than two players. But the noncooperative assumption is that players do not coordinate their strategy choices, so where do these correlations come from? The...

Persistent link: https://www.econbiz.de/10011206775

An Impossibility Theorem on Beliefs in Games

Brandenburger, Adam; Keisler, H. Jerome - In: The Language of Game Theory:Putting Epistemics into the …

A paradox of self-reference in beliefs in games is identified, which yields a game-theoretic impossibility theorem akin to Russell's Paradox. An informal version of the paradox is that the following configuration of beliefs is impossible:Ann believes that Bob assumes thatAnn believes that Bob's...

Persistent link: https://www.econbiz.de/10011206790

Creativity, probability and uncertainty

Wilson, Matthew - In: Journal of Economic Methodology 16 (2009) 1, pp. 45-56

Keynesian concepts of probability and uncertainty emphasize the basis of knowledge available to economic decision … makers. Conditions of uncertainty, which involve missing evidence or doubtful arguments, are distinguished from probable risk … among different kinds of uncertainty. The paper reviews this particular argument, distinguishing it from Keynesian …

Persistent link: https://www.econbiz.de/10004966913

A simple method of determining moments of a top event

Soman, K.P.; Misra, K.B. - In: International Journal of Quality & Reliability Management 13 (1996) 5, pp. 50-60

failure probability function nor its partial derivates to find these moments. This method has subsequently extended to systems …Describes a simple algorithm which has been developed for determining exact moments of top event failure probability … from the moments of the basic events in a fault tree. This method requires neither Taylor series expansion of top event …

Persistent link: https://www.econbiz.de/10014801074