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Algorithms for cautious reasoning in games. (English) Zbl 1430.91012

A cautious player in a noncooperative game takes into account all the strategies of the other players, even if they seem unlikely to be chosen. The question is what action should such player choose. Epistemic treatments of this problem make the outcome dependent on the reasoning process of the players.
Several procedures yield a solution under different assumptions on the epistemic states of the players. In this paper algorithms are used to model such reasoning processes in which each player’s preferences over her own strategies are completed by eliminating likelihood orderings (ordered partitions of the strategies of the other players).
These algorithms allow the comparison among well known solutions to the problem, like iterated admissibility, proper rationalizability and full permissibility, providing a sufficient condition under which differences emerge among the different solutions.
The algorithms are used to analyze an interesting example, namely a bilateral commitment bargaining game. It is shown, by means of the algorithms, that different solution notions prescribe different actions.

MSC:

91A10 Noncooperative games
91A26 Rationality and learning in game theory
91B26 Auctions, bargaining, bidding and selling, and other market models
91A68 Algorithmic game theory and complexity
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