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. 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
