Possibilistic Games with Incomplete Information

Bayesian games offer a suitable framework for games where the utility degrees are additive. This approach does nevertheless not apply to ordinal games, where the utility degrees do not capture more than a ranking, nor to situations of a decision under qualitative uncertainty. This paper proposes a representation framework for ordinal games under possibilistic incomplete information and extends the fundamental notion of Nash equilibrium (NE) to this framework. We show that deciding whether a NE exists is a difficult problem (NP-hard) and propose a Mixed Integer Linear Programming encoding. Experiments on variants of the GAMUT problems confirm the feasibility of this approach.