Abstract
We give a characterization of the equilibrium payoffs of a dynamic game, which is a stochastic game where the transition function is either one or zero and players can only use pure actions in each stage. The characterization is in terms of convex combinations of connected stationary strategies; since stationary strategies are not always connected, the equilibrium set may not be convex. We show that subgame perfection may reduce the equilibrium set.
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References
Aumann R, Shapley L (1976) Long term competition: A game theoretic analysis. Mimeo, Hebrew University
Ben-Porath E, Peleg B (1989) On the folk theorem and finite automata. Mimeo, Hebrew University
Bewley T, Kohlberg E (1976) The asymptotic theory of stochastic games. Mathematics of Operations Research 1
Duffie D, Geanakoplos J, Mas-Colell A, McLennan A (1994) Stationary Markov equilibrium. Econometrica 62
Friedman J (1989) A modified folk theorem for time-dependent supergames. Mimeo, University of North Carolina
Fudenberg D, Maskin E (1986) The folk theorem in repeated games with discounting or with incomplete information. Econometrica 54
Jovanovic B, Rosenthal R (1988) Anonymous sequential games. Journal of Mathematical Economics 17
Kalai E, Samet D, Stanford W (1986) Complexity in stochastic games. Northwestern University discussion paper
Lockwood B (1990) The folk theorem in stochastic games with and without discounting. Mimeo, Birkbeck College
Massó J (1993) Undiscounted equilibrium payoffs of repeated games with a continuum of players. Journal of Mathematical Economics 22
Mertens J-F, Parthasarathy T (1987) Equilibria for discounted stochastic games. Discussion Paper 8750, Center for Operations Research and Econometrics, Louvain
Rubinstein A (1977) Equilibrium in supergames. Mimeo, The Hebrew University
Shapley L (1953) Stochastic games. Proceedings of the National Academy of Sciences USA 39:1095–1100
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We are grateful to an anonymous referee for his very careful comments. Financial support from DGICYT grants PB89-0075, PB89-0294, and PB92-0590 and from Programa de Cooperación Cientifica Iberoamericana grant RD6841 is acknowledged.
The author gratefully acknowledges the support from CONICET: Republica Argentina. Financial support from Spain's Ministerio de Educación is also acknowledged.
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Massó, J., Neme, A. Equilibrium payoffs of dynamic games. Int J Game Theory 25, 437–453 (1996). https://doi.org/10.1007/BF01803950
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DOI: https://doi.org/10.1007/BF01803950