Possibilistic randomisation in strategic-form games

Since the seminal work of John Nash, convex combinations of actions are known to guarantee the existence of equilibria in strategic-form games. This paper introduces an alternative notion of randomisation among actions – possibilistic randomisation – and investigates the mathematical consequences of doing so. The framework of possibility theory gives rise to two distinct notions of equilibria both of which are characterised in our main results: a qualitative one based on the Sugeno integral and a quantitative one based on the Choquet integral. Then the two notions of equilibrium are compared against a coordination game with payoff-distinguishable equilibria known as the Weak-link game.

KEYWORDS: Possibilistic randomisation; Mixed strategies; Possibilistic expected utility; Nash equilibria; Weak-link game; Selection of multiple equilibria

Hosni, H and E. Marchioni. (2019). “Possibilistic randomisation in strategic-form gamesInternatonal Journal of Approximate Reasoning, 114, 204-225.  https://doi.org/10.1016/j.ijar.2019.08.008