ON NON-COOPERATIVE n-PERSON GAMES WITH SET PAYOFFS
Yousuke Araya, Yutaka Kimura, Masamichi Kon · Journal of the Operations Research Society of Japan · 2024
In this paper, non-cooperative n-person games with set payoffs are considered, where the payoffs are represented as non-empty subsets of ℓ-dimensional Euclidean space ℝℓ. First, several types of set relations on the set of all non-empty subsets of ℝℓ are defined. Next, several kinds of concepts of Nash equilibrium strategies for the games are defined by using the set relations. Then, the Nash equilibrium strategies are characterized by Nash equilibrium strategies for non-cooperative n-person games with scalar payoffs. The proposed theory described above can be interpreted as uncertain multi-objective game theory. We also formulate an uncertain multi-objective game.