Chapter 47 Stochastic games

Handbook of Game Theory with Economic Applications

Volumn 3, Issue , 2002, Pages 1809-1832

  Mertens, Jean François ^a  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

dynamic programming; games; non cooperative; stochastic; value

Indexed keywords

EID: 67649363664     PISSN: 15740005     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1574-0005(02)03010-2     Document Type: Review

References (62)

1. Amir R. Continuous stochastic games of capital accumulation with convex transitions. Games and Economic Behavior 15 (1996) 132-148
2. Bewley T., and Kohlberg E. The asymptotic theory of stochastic games. Mathematics of Operations Research 1 (1976) 197-208
3. Bewley T., and Kohlberg E. The asymptotic solution of a recursion equation occurring in stochastic games. Mathematics of Operations Research 1 (1976) 321-336
4. Bewley T., and Kohlberg E. On stochastic games with stationary optimal strategies. Mathematics of Operations Research 3 (1978) 104-125
5. Blackwell D. On randomization in statistical games with k terminal actions. In: Kuhn H.W., and Tucker A.W. (Eds). Contributions to the Theory of Games, Vol. II. Annals of Mathematics Studies Vol. 24 (1953), Princeton University Press 183-187
6. Blackwell D., and Ferguson T.S. The big match. Annals of Mathematical Statistics 39 (1968) 159-163
7. Charnes A., and Schroeder R. On some tactical antisubmarine games. Naval Research Logistics Quarterly 14 (1967) 291-311
8. Coulomb J.M. Repeated games with absorbing states and no signals. International Journal of Game Theory 21 (1992) 161-174
9. Duffie D., Geanakoplos J., Mas-Colell A., and McLennan A. Stationary Markov equilibria. Econometrica 62 (1994) 745-781
10. Dutta P., and Sundaram R. How different can strategic models be?. Journal of Economic Theory 60 (1993) 42-61
11. Everett H. Recursive games. In: Dresher M., Tucker A.W., and Wolfe P. (Eds). Contributions to the Theory of Games, Vol. III. Annals of Mathematics Studies Vol. 39 (1957), Princeton University Press, Princeton, NJ 47-78
12. Federgruen A. On N-person stochastic games with denumerable state space. Advances in Applied Probability 10 (1978) 452-471
13. Filar J.A. Player aggregation in the travelling inspector model. IEEE Transactions on Automatic Control AC-30 (1985) 723-729
14. Forges F. Infinitely repeated games of incomplete information: symmetric case with random signals. International Journal of Game Theory 11 (1982) 203-213
15. Forges F. An approach to communication equilibria. Econometrica 54 (1986) 1375-1385
16. Gilette D. Stochastic games with zero stop probabilities. In: Dresher M., Tucker A.W., and Wolfe P. (Eds). Contributions to the Theory of Games, Vol. III. Annals of Mathematics Studies Vol. 39 (1957), Princeton University Press, Princeton, NJ 179-187
17. Jacobson N. Lectures on Abstract Algebra Vol. I (1951), Van Nostrand, Princeton, NJ
18. Jacobson N. Lectures on Abstract Algebra Vol. II (1953), Van Nostrand
19. Jacobson N. Lectures on Abstract Algebra Vol. III (1964), Van Nostrand
20. Kohlberg E. Repeated games with absorbing states. Annals of Statistics 2 (1974) 724-738
21. Kohlberg E., and Neyman A. Asymptotic behavior of nonexpansive mappings in normed linear spaces. Israel Journal of Mathematics 38 (1981) 269-275
22. Kohlberg E., and Zamir S. Repeated games of incomplete information: the symmetric case. Annals of Statistics 2 (1974) 1010-1041
23. Lehrer E., and Monderer D. Discounting versus averaging in dynamic programming. Games and Economic Behavior 6 (1994) 97-113
24. Lehrer E., and Sorin S. A uniform Tauberian theorem in dynamic programming. Mathematics of Operations Research 17 (1992) 303-307
25. Leininger W. The existence of perfect equilibrium in a model of growth with altruism between generations. Review of Economic Studies 53 (1986) 349-367
26. Levhari D., and Mirman L. The Great Fish War: An example using a dynamic Cournot-Nash solution. Bell Journal of Economics 11 (1980) 322-334
27. Maitra A., and Parthasarathy T. On stochastic games. Journal of Optimization Theory and Applications 5 (1970) 289-300
28. Maitra A., and Sudderth W. An operator solution for stochastic games. Israel Journal of Mathematics 78 (1992) 33-49
29. Maitra A., and Sudderth W. Borel stochastic games with lim sup payoff. Annals of Probability 21 (1993) 861-885
30. Martin D. A purely inductive proof of Borel determinacy. In: Nerode A., and Shore R.A. (Eds). Recursion Theory, Proceedings of Symposia in Pure Mathematics Vol. 42 (1985), American Mathematical Society 303-308
31. Mertens J.-F. Repeated games: an overview of the zero-sum case. In: Hildenbrand W. (Ed). Advances in Economic Theory (1982), Cambridge University Press, Providence, RI 175-182
32. Mertens J.-F. Repeated games. In: Gleason A.M. (Ed). Proceedings of the International Congress of Mathematicians. Berkeley, 1986 (1987), American Mathematical Society, Cambridge, MA 1528-1577
33. Mertens J.-F. A measurable 'measurable choice' theorem. CORE Discussion Paper 8749 (1987), Université Catholique de Louvain, Providence, RI
34. Mertens J.-F., and Neyman A. Stochastic games. International Journal of Game Theory 10 2 (1981) 53-56
35. Mertens J.-F., and Neyman A. Stochastic games have a value. Proceedings of the National Academy of Sciences of the USA 79 (1982) 2145-2146
36. Mertens J.-F., and Parthasarathy T. Existence and characterisation of Nash equilibria for discounted stochastic games. CORE Discussion Paper 8750 (1987), Université Catholique de Louvain, Louvain-la-Neuve, Belgium
37. Mertens J.-F., and Parthasarathy T. Non-zero-sum stochastic games. In: Raghavan T.E.S., et al. (Ed). Stochastic Games and Related Topics (1991), Kluwer Academic, Louvain-la-Neuve, Belgium 145-148
38. Mertens J.-F., Sorin S., and Zamir S. Repeated games. CORE Discussion Papers 9420, 9421, 9422 (1994), Université Catholique de Louvain, Dordrecht
39. Mertens J.-F., and Zamir S. Formulation of Bayesian analysis for games with incomplete information. International Journal of Game Theory 14 (1985) 1-29
40. Milnor J., and Shapley L.S. On games of survival. In: Dresher M., Tucker A.W., and Wolfe P. (Eds). Contributions to the Theory of Games, Vol. III. Annals of Mathematics Studies Vol. 39 (1957), Princeton University Press, Louvain-la-Neuve, Belgium 15-45
41. Nowak A.S. Universally measurable strategies in zero-sum stochastic games. Annals of Probability 13 (1985) 269-287
42. Nowak A.S., and Raghavan T.E.S. Positive stochastic games and a theorem of Ornstein. In: Raghavan T.E.S., et al. (Ed). Stochastic Games and Related Topics (1991), Kluwer Academic, Princeton, NJ 127-134
43. Nowak A.S., and Raghavan T.E.S. Existence of stationary correlated equilibria with symmetric information for discounted stochastic games. Mathematics of Operations Research 17 (1992) 519-526
44. Parthasarathy T. Discounted, positive, and noncooperative stochastic games. International Journal of Game Theory 2 (1973) 25-37
45. Parthasarathy T. Markov games II. Methods of Operations Research 51 (1984) 369-376
46. Parthasarathy T., and Raghavan T.E.S. An order field property for stochastic games when one player controls transition probabilities. Journal of Optimization Theory and Applications 33 (1981) 375-392
47. Parthasarathy T., and Stern M. Markov games: A survey. In: Roxin E.O., Lin P.T., and Sternberg R.L. (Eds). Differential Games and Control Theory III, Lecture Notes in Pure and Applied Mathematics Vol. 30 (1976), Marcel Dekker, Dordrecht 1-46
48. In: Raghavan T.E.S., Ferguson T.S., Parthasarathy T., and Vrieze O.J. (Eds). Stochastic Games and Related Topics: In Honor of Professor L.S. Shapley (1991), Kluwer Academic, New York
49. Raghavan T.E.S., and Filar J.A. Algorithms for stochastic games: A survey. Zeitschrift für Operations Research, Methods and Models of Operations Research 35 (1991) 437-472
50. Shapley L.S. Stochastic games. Proceedings of the National Academy of Sciences of the USA 39 (1953) 1095-1100
51. Shubik M., and Whitt W. Fiat money in an economy with one nondurable good and no credit: A non-cooperative sequential game. In: Blaquière A. (Ed). Topics in Differential Games (1973), Elsevier, Dordrecht 401-448
52. Sobel M.J. Stochastic fishery games with myopic equilibria. In: Mirman L.J., and Spulber D. (Eds). Essays in the Economics of Renewable Resources (1982), Elsevier, Amsterdam
53. Sorin S. Asymptotic properties of a non-zero-sum stochastic game. International Journal of Game Theory 15 (1986) 101-107
54. Thuijsman F. Optimality and equilibria in stochastic games. Doctoraatsproefschrift, Rijksuniversiteit Limburg te Maastricht (1989)
55. Vieille N. Contributions à la théorie des jeux répétés. Ph.D. Thesis (1993), Université Paris 6, Amsterdam
56. Vrieze O.J. Linear programming and undiscounted stochastic games in which one player controls transitions. Operations Research Spektrum 3 (1981) 29-35
57. Vrieze O.J. Stochastic games with finite state and actions spaces. Ph.D. Thesis (1983), Catholic University of Nijmegen, Paris
58. Vrieze O.J., and Thuijsman F. Stochastic games and optimal stationary strategies. A survey. Report 8639 (1986), Department of Mathematics, University of Nijmegen, The Netherlands
59. Vrieze O.J., and Thuijsman F. On equilibria in repeated games with absorbing states. International Journal of Game Theory 18 (1989) 293-310
60. Vrieze O.J., Tijs S.H., Raghavan T.E.S., and Filar J.A. A finite algorithm for switching control stochastic games. Operations Research Spektrum 5 (1983) 15-24
61. Winston W. A stochastic game model of a weapons development competition. SIAM Journal of Control and Optimization 16 (1978) 411-419
62. mimeo. Winston W., and Cabot A.V. A stochastic game model of football play selection (1984), Indiana University, The Netherlands