Ultimatum Games and Fuzzy Information

We consider the proposer's decision process in an ultimatum game where his uncertainty with respect to the responder's preferences and the associated acceptance threshold is modeled by a fuzzy set. Employing a three-step defuzzification strategy we determine the proposer's best possible claim which depends on his beliefs and his attitude towards risk. Furthermore, we derive an explicit solution for a specific class of fuzzy sets. From a more abstract point of view we analyze a game in which one player has a non-continuous objective function and where the uncertain point of discontinuity is determined by the other player's strategy.

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