Compact preference representation and Boolean games

Game theory is a widely used formal model for studying strategical interactions between agents. Boolean games (Harrenstein, Logic in conflict, PhD thesis, 2004; Harrenstein et al., Theoretical Aspects of Rationality and Knowledge, pp. 287–298, San Francisco Morgan Kaufmann, 2001) yield a compact representation of 2-player zero-sum static games with binary preferences: an agent’s strategy consists of a truth assignment of the propositional variables she controls, and a player’s preferences are expressed by a plain propositional formula. These restrictions (2-player, zero-sum, binary preferences) strongly limit the expressivity of the framework. We first generalize the framework to n-player games which are not necessarily zero-sum. We give simple characterizations of Nash equilibria and dominated strategies, and investigate the computational complexity of the associated problems. Then, we relax the last restriction by coupling Boolean games with a representation, namely, CP-nets.

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