Operator approach to values of stochastic games with varying stage duration

• Brézis H (1973) Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert, North-Holland

• Brézis H, Pazy A (1970) Accretive sets and differential equations in Banach spaces. Isr J Math 8:367–383

  Article  Google Scholar 

• Guo X, Hernandez-Lerma O (2003) Zero-sum games for continuous-time Markov chains with unbounded transition and average payoff rates. J Appl Probab 40:327–345

  Article  Google Scholar 

• Guo X, Hernandez-Lerma O (2005) Zero-sum continuous-time Markov games with unbounded transition and discounted payoff rates. Bernoulli 11:1009–1029

  Article  Google Scholar 

• Kolokoltsov VN (1992) On linear, additive, and homogeneous operators in idempotent analysis. In: Maslov VP, Samborski SN (eds) Advances in Soviet Mathematics, vol 13. Idempotent analysis, pp 87–101

• Mertens J-F, Sorin S, Zamir S (2015) Repeated games. Cambridge University Press, Cambridge

  Book  Google Scholar 

• Miyadera I, Oharu S (1970) Approximation of semi-groups of nonlinear operators. Tôhoku Math J 22:24–47

  Article  Google Scholar 

• Neyman A (2003) Stochastic games and nonexpansive maps. In: Neyman A, Sorin S (eds) Stochastic games and applications. NATO science series, vol C 570. Kluwer Academic Publishers, pp 397–415

• Neyman A (2012) Continuous-time stochastic games, DP 616. CSR, Jerusalem

  Google Scholar 

• Neyman A (2013) Stochastic games with short-stage duration. Dyn Games Appl 3:236–278

  Article  Google Scholar 

• Neyman A, Sorin S (2010) Repeated games with public uncertain duration process. Int J Game Theory 39:29–52

  Article  Google Scholar 

• Nowak AS (1985) Universally measurable strategies in zero-sum stochastic games. Ann Probab 13:269–287

  Article  Google Scholar 

• Nowak AS (2003) Zero-sum stochastic games with Borel state spaces. In: Neyman A,Sorin S (eds) Stochastic games and applications. NATO science series, vol C 570. Kluwer Academic Publishers, pp 77–91

• Prieto-Rumeau T, Hernandez-Lerma O (2012) Selected topics on continuous-time controlled Markov chains and Markov games. Imperial College Press, London

  Google Scholar 

• Rosenberg D, Sorin S (2001) An operator approach to zero-sum repeated games. Isr J Math 121:221–246

  Article  Google Scholar 

• Shapley LS (1953) Stochastic games. Proc Natl Acad Sci USA 39:1095–1100

• Sorin S (2003) The operator approach to zero-sum stochastic games. In: Neyman A, Sorin S (eds) Stochastic games and applications. NATO science series, vol C 570. Kluwer Academic Publishers, pp 375–395

• Sorin S (2004) Asymptotic properties of monotonic nonexpansive mappings. Discrete Event Dyn Syst 14:109–122

  Article  Google Scholar 

• Sorin S (2015) Limit value of dynamic zero-sum games with vanishing stage duration, preprint

• Tanaka K, Wakuta K (1977) On continuous Markov games with the expected average reward criterion. Sci Rep Niigata Univ Ser A 14:15–24

  Google Scholar 

• Vigeral G (2009) Propriétés asymptotiques des jeux répétés à somme nulle, PhD Thesis, UPMC-Paris 6

• Vigeral G (2010) Evolution equations in discrete and continuous time for non expansive operators in Banach spaces. ESAIM COCV 16:809–832

  Article  Google Scholar 

• Vigeral G (2013) A zero-sum stochastic game with compact action sets and no asymptotic value. Dyn Games Appl 3:172–186

  Article  Google Scholar 

• Zachrisson LE (1964) Markov games. In: Dresher M, Shapley LS, Tucker AW (eds) Advances in game theory. Annals of mathematical studies, vol 52. Princeton University Press, pp 210–253

• Ziliotto B (2013) Zero-sum repeated games: counterexamples to the existence of the asymptotic value and the conjecture \(maxmin=lim v_{n}\), preprint hal-00824039, to appear in Annals of Probability

Download references