Limit equilibrium payoffs in Stochastic Games

Jérôme Renault (1) , Bruno Ziliotto (2)

1 TSE-R - Toulouse School of Economics
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We study the limit of equilibrium payoffs, as the discount factor goes to one, in nonzero-sum stochastic games. We first show that the set of stationary equilibrium payoffs always converges. We then provide 2-player examples in which the whole set of equilibrium payoffs diverges. The construction is robust to perturbations of the payoffs, and to the introduction of normal-form correlation.

Mots clés: Stochastic games; Limit equilibrium payoffs; Folk theorem

Domaines: Mathématiques [math]

Jérôme Renault, Bruno Ziliotto. Limit equilibrium payoffs in Stochastic Games. Mathematics of Operations Research, 2020, 45 (3), pp.889-895. ⟨10.1287/moor.2019.1015⟩. ⟨hal-04041893⟩