Zero-sum repeated games: Counterexamples to the existence of the asymptotic value and the conjecture maxmin=limvn

• Ziliotto, Bruno ^[1]
  1. [1] Toulouse 1 Capitole University

     Toulouse 1 Capitole University

     Arrondissement de Toulouse, Francia

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 2, 2016, págs. 1107-1133
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • Mertens [In Proceedings of the International Congress of Mathematicians (Berkeley, Calif., 1986) (1987) 1528–1577 Amer. Math. Soc.] proposed two general conjectures about repeated games: the first one is that, in any two-person zero-sum repeated game, the asymptotic value exists, and the second one is that, when Player 1 is more informed than Player 2, in the long run Player 1 is able to guarantee the asymptotic value. We disprove these two long-standing conjectures by providing an example of a zero-sum repeated game with public signals and perfect observation of the actions, where the value of the λ-discounted game does not converge when λ goes to 0. The aforementioned example involves seven states, two actions and two signals for each player. Remarkably, players observe the payoffs, and play in turn.