Possibilistic Games with Incomplete Information

Possibilistic Games with Incomplete Information

Nahla Ben Amor, Helene Fargier, Régis Sabbadin, Meriem Trabelsi

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence
Main track. Pages 1544-1550. https://doi.org/10.24963/ijcai.2019/214

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. This paper proposes a representation framework for ordinal games under possibilistic incomplete information (π-games) 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  (MILP) encoding. Experiments on variants of the GAMUT problems confirm the feasibility of this approach.
Keywords:
Knowledge Representation and Reasoning: Qualitative Reasoning
Agent-based and Multi-agent Systems: Noncooperative Games
Uncertainty in AI: Uncertainty in AI
Knowledge Representation and Reasoning: Knowledge Representation and Game Theory ; Social Choice
Agent-based and Multi-agent Systems: Algorithmic Game Theory
Uncertainty in AI: Nonprobabilistic Models