Abstract
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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