Optimal strategies in a class of zero-sum ergodic stochastic games

Mathematical Methods of Operations Research

Volumn 50, Issue 3, 1999, Pages 399-419

  Nowak, Andrzej S ^a  

^a WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Average optimal strategies; Borel state space; Discrete time zero sum stochastic games; Overtaking optimal strategies

Indexed keywords

EID: 0001386709     PISSN: 14322994     EISSN: None     Source Type: Journal    
DOI: 10.1007/s001860050078     Document Type: Article

References (39)

1. Altman E (1996) Nonzero-sum stochastic games in admission, service and routing control in queueing systems. QUESTA 23:259-279
2. Altman E, Hordijk A (1995) Zero-sum Markov games and worst-case optimal control of queueing systems. QUESTA 21:415-447
3. Altman E, Hordijk A, Spieksma FM (1997) Contraction conditions for average and a-discount optimality in countable state Markov games with unbounded rewards. Math. Oper. Res. 22:588-618
4. Bertsekas DP, Shreve SE (1978) Stochastic optimal control: the discrete time case. Academic Press, New York
5. Borkar VS, Ghosh MK (1993) Denumerable state stochastic games with limiting average payoff. J. Optim. Theory Appl. 76:539-560
6. Brown BW (1965) On the iterative method of dynamic programming on a finite space discrete time Markov processes. Ann. Math. Statist. 36:1279-1285
7. Carlson D, Haurie A, Leizarowitz A (1994) Overtaking equilibria for switching regulator and tracking games. In: Haurie (eds.) Advances in Dynamic Games and Applications, Haurie (eds.) Basar T, Annals of Dynamic Games 1:247-268
8. Couwenbergh HAM (1980) Stochastic games with metric state space. Internat. J. Game Theory 9:25-36
9. Dunford N, Schwartz JT (1958) Linear operators, Vol.I. Interscience Publishers, New York
10. Fan K (1953) Minimax theorems. Proc. Nat. Acad. Sci. USA 39:42-47
11. Flynn J (1980) On optimality criteria for dynamic programs with long finite horizons. J. Math. Anal. Appl. 76:202-208
12. Gale D (1967) On optimal development in a multisector economy. Rev. Econ. Studies 34:1-19
13. Gordienko E, Hernández-Lerma O (1995) Average cost Markov control processes with weighted norms: existence of canonical policies. Appl. Mathematicae 23:199-218
14. Gordienko E, Hernández-Lerma O (1995) Average cost Markov control processes with weighted norms: value iteration. Appl. Mathematicae 23:219-237
15. Hernández-Lerma O, Lasserre JB (1996) Discrete-time Markov control processes: basic optimality criteria. Springer-Verlag, New York
16. Hernández-Lerma O, Vega-Amaya O (1998) Infinite horizon Markov control processes with undiscounted cost criteria: from average to overtaking optimality. Applicationes Mathematicae 25:153-178
17. Küenle H-U (1986) Stochastische Spiele und Entscheidungsmodelle. Teubner-Texte zur Mathematik 89, Teubner-Verlag, Leipzig
18. Küenle H-U (1996) Stochastic games with complete information and average cost criterion. The Annals of Dynamic Games, forthcoming
19. Leizarowitz A (1996) Overtaking and almost-sure optimality in infinite horizon Markov decision processes. Math. Oper. Res. 21:158-181
20. Maitra A, Sudderth WD (1993) Borel stochastic games with limsup payoff. Ann. Probab. 21:861-885
21. Mertens JF, Neyman A (1981) Stochastic games. Internat. J. Game Theory 10:53-66
22. Meyn SP, Tweedie RL (1993) Markov chains and stochastic stability. Springer-Verlag, New York
23. Meyn SP, Tweedie RL (1994) Computable bounds for geometric convergence rates of Markov chains. Ann. Appl. Probab. 4:981-1011
24. Nowak AS (1984) On zero-sum stochastic games with general state space I. Probab. Math. Statist. 4:13-32
25. Nowak AS (1985) Measurable selection theorems for minimax stochastic optimization problems. SIAM J. Control Optim. 23:466-476
26. Nowak AS (1985) Universally measurable strategies in zero-sum stochastic games. Ann. Probab. 13:269-287
27. Nowak AS (1992) Stationary overtaking optimal strategies in Markov decision processes with general state spaces. Technical Report, Institute of Mathematics, Wroclaw University of Technology, Poland
28. Nowak AS (1994) Zero-sum average payoff stochastic games with general state space. Games and Econ. Behavior 7:221-232
29. Nowak AS (1999) Sensitive equilibria for ergodic stochastic games with countable state spaces. Math Meth Oper Res 50:65-76
30. Nowak AS, Altman E (1998) ε-Nash equilibria for stochastic games with uncountable state space and unbounded cost. Technical Report, Institute of Mathematics, Wroclaw University of Technology, Poland
31. Nowak AS, Vega-Amaya O (1999) A counterexample on overtaking optimality. Math Meth Oper Res 49:435-439
32. Ramsey FP (1928) A mathematical theory of savings. Economic J. 38:543-559
33. Rieder U (1978) On semi-continuous dynamic games. Technical Report, Department of Mathematics, University of Karlsruhe
34. Rieder U (1979) Equilibrium plans for nonzero-sum Markov games. In: Moeschlim O, Pallaschke D (eds.) Game Theory and Related Topics, North-Holland, Amsterdam, pp. 91-102
35. Rieder U (1995) Average optimality in Markov games with general state space. Proceedings of the 3rd Internat. Conference on Approximation Theory and Optimization, Puebla, Mexico
36. Royden HL (1968) Real analysis. MacMillan, London
37. Rubinstein A (1979) Equilibria in supergames with the overtaking criterion. J. Economic Theory 21:1-9
38. Sennott LI (1994) Zero-sum stochastic games with unbounded cost: discounted and average cost cases. Z. Oper. Res. 39:209-225
39. von Weizsäcker CC (1965) Existence of optimal programs of accumulation for an infinite horizon. Review of Econom. Studies 32:85-104