Stationary equilibria in stochastic games: Structure, selection, and computation

Journal of Economic Theory

Volumn 118, Issue 1, 2004, Pages 32-60

  Herings, P Jean Jacques ^a   Peeters, Ronald J A P ^a  

^a MAASTRICHT UNIVERSITY   (Netherlands)

Author keywords

Computation of equilibria; Game theory; Linear tracing procedure; Stochastic games

Indexed keywords

EID: 4344678574     PISSN: 00220531     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jet.2003.10.001     Document Type: Article

References (39)

1. Bergemann D. Välimäki J. Learning and strategic pricing Econometrica 64 1996 1125-1149
2. Breton M. Algorithms for stochastic games, In: Raghavan T.E.S. Ferguson T.S. Parthasarathy T. Vrieze O.J. (Eds.). Stochastic Games and Related Topics: In Honor of Professor L.S. Shapley Theory and Decision Library C: Game Theory, Mathematical Programming and Operations Research Vol. 7 1991 45-57 Kluwer Academic Publishers Dordrecht
3. Breton M. Filar J.A. Haurie A. Schultz T.A. On the computation of equilibria in discounted games, In: Basar T. (Ed.). Dynamic Games and Applications in Economics Lecture Notes on Economics and Mathematical Systems Vol. 205 1986 Springer Berlin
4. van den Elzen A.H. Talman A.J.J. An algorithmic approach towards the tracing procedure for bi-matrix games Games Econ. Behav. 28 1999 130-145
5. Filar J.A. Schultz T.A. Thuijsman F. Vrieze O.J. Nonlinear programming and stationary equilibria in stochastic games Math. Prog. 50 1991 227-237
6. Fink A.M. Equilibrium in a stochastic n-person game J. Sci. Hiroshima Univ. Series A-I 28 1964 89-93
7. Garcia C.B. Zangwill W.I. Pathways to Solutions, Fixed Points, and Equilibria 1981 Prentice-Hall Englewood Cliffs, NJ
8. Haller H. Lagunoff R. Genericity and Markovian behavior in stochastic games Econometrica 68 2000 1231-1248
9. Harsanyi J.C. Oddness of the number of equilibrium points Int. J. Game Theory 2 1973 235-250
10. Harsanyi J.C. Selten R. A general theory of equilibrium selection in games 1988 MIT Press Cambridge, MA
11. Herings P.J.J. A globally and universally stable price adjustment process J. Math. Econ. 27 1997 163-193
12. Herings P.J.J. Two simple proofs of the feasibility of the linear tracing procedure Econ. Theory 15 2000 485-490
13. Herings P.J.J. van den Elzen A.H. Computation of the Nash equilibrium selected by the tracing procedure in n-person games Games Econ. Behav. 38 2001 89-117
14. Herings P.J.J. Peeters R.J.A.P. A differentiable homotopy to compute Nash equilibria of n-person games Econ. Theory 18 2001 159-185
15. P.J.J. Herings, R.J.A.P. Peeters, Equilibrium selection in stochastic games, METEOR Research Memorandum 01/019, Universiteit Maastricht, Maastricht, 2001, Int. Game Theory Rev., forthcoming
16. n Methoden und Verfahren der mathematische Physik Vol. 29 1983 Peter Lang Frankfurt
17. Judd K.L. Computational economics and economic theory: Substitutes and complements? J. Econ. Dynam. Control 21 1997 907-942
18. Lemke C.E. Howson J.T. Jr. Equilibrium points of bimatrix games SIAM J. Appl. Math. 12 1964 413-423
19. Mas-Colell A. The Theory of General Economic Equilibrium: A Differentiable Approach 1985 Cambridge University Press Cambridge
20. Maskin E. Tirole J. Markov perfect equilibrium, I: Observable actions J. Econ. Theory 100 2001 191-219
21. R.D. McKelvey, A. McLennan, Computation of equilibria in finite games, in: H.M. Amman, D.A. Kendrick, J. Rust (Eds.), Handbook of Computational Economics, Vol. I, Elsevier Science, Amsterdam, 1996, pp. 87-142
22. McKelvey R.D. Palfrey T.R. Quantal response equilibria for normal form games Games Econ. Behav. 10 1995 6-38
23. McKelvey R.D. Palfrey T.R. Quantal response equilibria in extensive form games Exper. Econ. 1 1998 9-41
24. A. McLennan, The expected number of Nash equilibria of a normal form game, Mimeo, 1999
25. Olley G.S. Pakes A. The dynamics of productivity in the telecommunications equipment industry Econometrica 64 1996 1263-1298
26. Pakes A. Ericson R. Empirical implications of alternative models of firm dynamics J. Econ. Theory 79 1989 1-45
27. Pakes A. McGuire P. Stochastic algorithms, symmetric Markov perfect equilibrium, and the 'curse' of dimensionality Econometrica 69 2001 1261-1282
28. Parthasarathy T. Raghavan T.E.S. An orderfield property for stochastic games when one player controls transition probabilities J. Opt. Theory Appl. 33 1981 375-392
29. Rosenmüller J. On a generalization of the Lemke - Howson algorithm to noncooperative n-person games SIAM J. Appl. Math. 21 1971 73-79
30. Scarf H. The approximation of fixed points of a continuous mapping SIAM J. Appl. Math. 15 1967 1328-1343
31. T.A. Schultz, Mathematical Programming and Stochastic Games, Ph.D. thesis, The John Hopkins University, Baltimore, MD, 1986
32. Shapley L.S. Stochastic games Proc. Natl. Acad. Sci. USA 39 1953 1095-1100
33. Sobel M.J. Non-cooperative stochastic games Ann. Math. Statist. 42 1971 1930-1935
34. von Stengel B. van den Elzen A.H. Talman A.J.J. Computing normal form perfect equilibria for extensive two-person games Econometrica 70 2002 693-715
35. Takahashi M. Equilibrium points of stochastic, noncooperative n-person games J. Sci. Hiroshima Univ. Series A-I 28 1964 95-99
36. 2 maps Appl. Math. Comput. 5 1979 297-311
37. Watson L.T. Billups S.C. Morgan A.P. HOMPACK: A suite of codes for globally convergent homotopy algorithms ACM Trans. Math. Software 13 1987 281-310
38. 2 maps ACM Trans. Math. Software 6 1980 252-260
39. Wilson R. Computing equilibria of n-person games SIAM J. Appl. Math. 21 1971 80-87