Possibility and Permissibility
Mathematical Social Sciences ,62 (2011), pp.109-113
Abstract: We formulate the permissibility concept (Brandenburger, 1992) in terms of general preference, and prove that the solution concept characterizes rationality, caution, and common "belief" of rationality and caution.
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Correlated Nash Equilibrium
Journal of Economic Theory , 144 (2009), pp.722-743
Abstract: We modify the epistemic conditions for Nash equilibrium only to accommodate Gilboa and Schmeidler's [I. Gilboa, D. Schmeidler, Maxmin expected utility with nonunique prior, J. Math. Econ. 18 (1989) 141-153] maxmin expected utility preferences, and identify the equilibrium concept in n-player strategic games that characterizes the modified epistemic conditions. The epistemic characterization supports the equilibrium concept as a minimal generalization of Nash equilibrium, in the sense that it deviates from Nash equilibrium only in terms of players' attitude towards ambiguity. Consequently, comparing it with Nash equilibrium constitutes a ceteris paribus study of the effects of ambiguity on how a game is played. For example, with ambiguity, (beliefs about) action choices are in general correlated.
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Extensive Form Games with Uncertainty Averse Players
Games and Economic Behavior , 28 (1999), pp.256-270
Abstract: Existing equilibrium concepts for games make use of the subjective expected utility model axiomatized by Savage (1954) to represent players' preferences. Accordingly, each player's beliefs about the strategies played by opponents are represented by a probability measure. Motivated by the Ellsberg Paradox and relevant experimental findings demonstrating that the beliefs of a decision maker may not be representable by a probability measure, this paper generalizes Nash Equilibrium in finite extensive form games to allow for preferences conforming to the multiple priors model developed in Gilboa and Schmeidler (1989). The implications of this generalization for strategy choices and welfare are studied.
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Sealed Bid Auctions with Uncertainty Averse Bidders
Economic Theory , 12 (1998), pp.1-20
Abstract: Traditional analysis of auctions assumes that each bidder's beliefs about opponents' valuations are represented by a probability measure. Motivated by experimental findings such as the Ellsberg Paradox, this paper examines the consequences of relaxing this assumption in the first and second price sealed bid auctions with independent private values. The multiple priors model of Gilboa and Schmeidler [Journal of Mathematical Economics, 18 (1989), 141-153] is adopted specifically to represent the bidders' (and the auctioneer's) preferences. The unique equilibrium bidding strategy in the first price auction is derived. Moreover, under an interesting parametric specialization of the model, it is shown that the first price auction Pareto dominates the second price auction.
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Weighted and Quadratic Models of Choice under Uncertainty
Economics Letters , 50 (1996), pp.381-386
Abstract: This paper extends the weighted and quadratic utility models of choice under risk to the context of choice under uncertainty. An important characteristic of the models is that they admit 'dynamically consistent' updating rules.
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Equilibrium in Beliefs under Uncertainly
Journal of Economic Theory , 71(2), 1996, pp.443-484
Abstract: Existing equilibrium concepts for games make use of the subjective expected utility model axiomatized by Savage (1954) to represent players' preferences. Accordingly, each player's beliefs about the strategies played by opponents are represented by a probability measure. Motivated by experimental findings such as the Ellsberg Paradox demonstrating that the beliefs of a decision maker may not be representable by a probability measure, this paper generalizes equilibrium concepts for normal form games to allow for the beliefs of each player to be representable by a closed and convex set of probability measures. The implications of this generalization for the strategy choices and welfare of players are studied.
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