Games of Incomplete Information: A Framework Based on Belief Functions

Hélène Fargier (1) , Érik Martin-Dorel (2) , Pierre Pomeret-Coquot (1, 2)

1 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
2 IRIT-ACADIE - Assistance à la Certification d’Applications DIstribuées et Embarquées

This paper proposes a model for incomplete games where the knowledge of the players is represented by a Dempster-Shafer belief function. Beyond an extension of the classical definitions, it shows such a game can be transformed into an equivalent hypergraphical complete game (without uncertainty), thus generalizing Howson and Rosenthal’s theorem to the framework of belief functions and to any number of players. The complexity of this transformation is finally studied and shown to be polynomial in the degree of k-additivity of the mass function.

Mots clés: Game theory; Incomplete games; Belief functions

Domaines: Intelligence artificielle [cs.AI]; Complexité [cs.CC]

Hélène Fargier, Érik Martin-Dorel, Pierre Pomeret-Coquot. Games of Incomplete Information: A Framework Based on Belief Functions. 16th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2021), Sep 2021, Prague, Czech Republic. pp.328-341, ⟨10.1007/978-3-030-86772-0_24⟩. ⟨hal-03382397⟩