Hailin Liu

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Rationalizability under Uncertainty using Imprecise Probabilities

Abstract

The notion of imprecise probability can be viewed as a generalization of the traditional notion of probability. Several theories and models of imprecise probability have been suggested in the literature as more appropriate representations of uncertainty in the context of single-agent decision making. In this paper we investigate the question of how such models can be incorporated into the traditional game-theoretic framework. In the spirit of rationalizability, we present a new solution concept called Gamma-maximin rationalizability that captures the idea that each player models the other players as decision makers who all employ Gamma-maximin as their decision rule. Some properties of this concept such as existence conditions and the relationship with rationalizability are studied.

Keywords

Game theory, imprecise probabilities, rationalizability, Gamma-maximin rationalizability

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E-mail addresses

Hailin Liu

hailinl@andrew.cmu.edu