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Article Dans Une Revue International Journal of Approximate Reasoning Année : 2022

Solving possibilistic games with incomplete information

Résumé

Bayesian games offer a suitable framework for games where the utility degrees are additive in essence. This approach does nevertheless not apply to ordinal games, where the utility degrees do not capture more than a ranking, nor to situations of decision under qualitative uncertainty. The present paper proposes a representation framework for ordinal games under possibilistic incomplete information and extends the fundamental notions of pure and mixed Nash equilibrium to this framework. We show that deciding whether a pure Nash equilibrium exists is a difficult task (NP-hard) and propose a Mixed Integer Linear Programming (MILP) encoding of the problem; as to the problem of computing a possibilistic mixed equilibrium, we show that it can be solved in polynomial time. An experimental study based on the GAMUT game generator confirms the feasibility of the approach.
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Dates et versions

hal-03744954 , version 1 (02-09-2022)
hal-03744954 , version 2 (02-09-2022)

Identifiants

Citer

Nahla Ben Amor, Hélène Fargier, Régis Sabbadin, Meriem Trabelsi. Solving possibilistic games with incomplete information. International Journal of Approximate Reasoning, 2022, 143 (C), pp.139 - 158. ⟨10.1016/j.ijar.2022.01.009⟩. ⟨hal-03744954v2⟩
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