186 research outputs found
EPISTEMIC FOUNDATIONS OF SOLUTION CONCEPTS IN GAME THEORY: AN INTRODUCTION
No full textWe give an introduction to the literature on the epistemic foundations of solution concepts in game theory. Only normal-form games are considered. The solution concepts analyzed are rationalizability, strong rationalizability, correlated equilibrium and Nash equilibrium. The analysis is carried out locally in terms of properties of the belief hierarchies. Several examples are used throughout to illustrate definitions and concepts.
Verhüllen und Verbergen – Strategien der Sakralisierung und der Mystifizierung von und mit Reliquien
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A THEORY OF RATIONAL CHOICE UNDER COMPLETE IGNORANCE
No full textThis paper contributes to a theory of rational choice under uncertainty for decision-makers whose preferences are exhaustively described by partial orders representing ""limited information."" Specifically, we consider the limiting case of ""Complete Ignorance"" decision problems characterized by maximally incomplete preferences and important primarily as reduced forms of general decision problems under uncertainty. ""Rationality"" is conceptualized in terms of a ""Principle of Preference-Basedness,"" according to which rational choice should be isomorphic to asserted preference. The main result characterizes axiomatically a new choice-rule called ""Simultaneous Expected Utility Maximization"" which in particular satisfies a choice-functional independence and a context-dependent choice-consistency condition; it can be interpreted as the fair agreement in a bargaining game (Kalai-Smorodinsky solution) whose players correspond to the different possible states (respectively extermal priors in the general case).
INTRODUCTION TO THE SEMANTICS OF BELIEF AND COMMON BELIEF
No full textWe provide an introduction to interactive belief systems from a qualitative and semantic point of view. Properties of belief hierarchies are formulated locally. Among the properties considered are ""Common belief in no error"" (which has been shown to have important game theoretic applications), ""Negative introspection of common belief"" and ""Truth about common belief."" The relationship between these properties is studied.
Preference for Flexibility and Freedom of Choice in a Savage Framework
No full textIn this paper, we study preferences over Savage acts that map states to opportunity sets. Conditional preferences over opportunity sets may be inconsistent with indirect-utility maximization due to implicit uncertainty about future preferences (preference for flexibility), or to an intrinsic preference for freedom of choice. On a flexibility interpretation, the main result characterizes preferences based on maximizing the expected indirect utility in terms of an ""Indirect Stochastic Dominance"" axiom. The relevance of the result to a freedom-of-choice context is established on the basis of a novel multi-attribute conceptualization of the notion of effective freedom of choice; the theorem delivers an additive multi-attribute representation with optimal uniqueness properties. The key technical tool of the paper, a version of MÅ¡bius inversion has been imported from the theory of (non-additive) ""belief-functions;"" it also yields a simple and intuitive proof of Kreps''s (1979) classic result.
INCENTIVE-COMPATIBLE AND EFFICIENT RESOURCE ALLOCATION IN LARGE ECONOMIES: AN EXACT AND LOCAL APPROACH
No full textThe main result of this paper characterizes possibly non-symmetric strategy-proof and efficienct choice functions as Perfectly Competitive. Efficiency is defined as impossibility of improvement by reallocation of commodity among finite sets of agents, and largeness of the economy is captured by a weak aggregation-condition called ""local separability."" Individual rationality constraints with respect to an assignment of endowments imply that the resulting allocations must be Walrasian relative to the assignment of endowments. The exact, local approach combined with a normality assumption on the domain of preferences allows the proofs to remain elementary throughout.
AGREEING TO DISAGREE: A SURVEY
No full textAumann (1976) put forward a formal definition of common knowledge and used it to prove that two ""like minded"" individuals cannot ""agree to disagree"" in the following sense. If they start from a common prior and update the probability of an event E (using Bayes'' rule) on the basis of private information, then it cannot be common knowledge between them that individual 1 assigns probability p to E and individual 2 assigns probability q to E with p ¹ q. In other words, if their posteriors of event E are common knowledge then they must coincide. Aumann''s Agreement Theorem has given rise to a large literature which we review in this paper. The results are classified according to whether they are probabilistic (Bayesian) or qualitative. Particular attention is paid to the issue of how to interpret the notion of Harsanyi consistency as a (local) property of belief hierarchies.
CAPACITIES AND PROBABILISTIC BELIEFS: A PRECARIOUS COEXISTENCE
No full textThis paper raises the problem of how to define revealed probabilistic beliefs in the context of the capacity/Choquet Expected Utility model. At the center of the analysis is a decision-theoretically axiomatized definition of ""revealed unambiguous events."" The definition is shown to impose surprisingly strong restrictions on the underlying capacity and on the set of unambiguous events; in particular, the latter is always an algebra. Alternative weaker definitions violate even minimal criteria of adequacy. Rather than finding fault with the proposed definition, we argue that our results indicate that the CEU model is epistemically restrictive, and point out that analogous problems do not arise within the Maximin Expected Utility model.
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