VALUE AND EQUILIBRIUM

Sylvain Sorin (1)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

We compare the two basic concepts of minmax value and equilibrium points in terms of :-definitions, properties and interpretation,-tools used in the existence proofs,-developments and applications, in particular for repeated games. This will lead us to question the approach asserting the following viewpoint: Equilibrium as extension of the value paradigm to non-zero sum games, Value as a special case of equilibrium payoff for zero-sum games. We claim that many important properties apply only to one of these concepts. 1. BASIC CONCEPTS We first recall the framework and the definition of these fundamental notions: value and equilibria.

Domaines: Optimisation et contrôle [math.OC]; Mathématiques [math]

Sylvain Sorin. VALUE AND EQUILIBRIUM. 2022. ⟨hal-03910014⟩