On the Existence of Markov Perfect Equilibria in Perfect Information Games
AbstractWe study the existence of pure strategy Markov perfect equilibria in two-person perfect information games. There is a state space X and each period player's possible actions are a subset of X. This set of feasible actions depends on the current state, which is determined by the choice of the other player in the previous period. We assume that X is a compact Hausdorff space and that the action correspondence has an acyclic and asymmetric graph. For some states there may be no feasible actions and then the game ends. Payoffs are either discounted sums of utilities of the states visited, or the utility of the state where the game ends. We give sufficient conditions for the existence of equilibrium e.g. in case when either feasible action sets are finite or when players' payoffs are continuously dependent on each other. The latter class of games includes zero-sum games and pure coordination games.
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Bibliographic InfoPaper provided by Aboa Centre for Economics in its series Discussion Papers with number 68.
Date of creation: Oct 2011
Date of revision:
dynamic games; Markov perfect equilibrium;
Find related papers by JEL classification:
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-03-08 (All new papers)
- NEP-GTH-2012-03-08 (Game Theory)
- NEP-HPE-2012-03-08 (History & Philosophy of Economics)
- NEP-MIC-2012-03-08 (Microeconomics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Borgers, Tilman, 1989. "Perfect equilibrium histories of finite and infinite horizon games," Journal of Economic Theory, Elsevier, vol. 47(1), pages 218-227, February.
- Kuipers, J. & Flesch, J. & Schoenmakers, G. & Vrieze, K., 2009. "Pure subgame-perfect equilibria in free transition games," European Journal of Operational Research, Elsevier, vol. 199(2), pages 442-447, December.
- Hannu Salonen & Hannu Vartiainen, 2005.
"On the Existence of Undominated Elements of Acyclic Relations,"
Game Theory and Information
- Salonen, Hannu & Vartiainen, Hannu, 2010. "On the existence of undominated elements of acyclic relations," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 217-221, November.
- Livshits, Igor, 2002. "On non-existence of pure strategy Markov perfect equilibrium," Economics Letters, Elsevier, vol. 76(3), pages 393-396, August.
- V. Bhaskar & George J. Mailath & Stephen Morris, 2012.
"A Foundation for Markov Equilibria in Infinite Horizon Perfect Information Games,"
PIER Working Paper Archive
12-043, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
- V. Bhaskar & George J. Mailathy & Stephen Morris, 2009. "A Foundation for Markov Equilibria in Infinite Horizon Perfect Information Games," Levine's Working Paper Archive 814577000000000178, David K. Levine.
- V. Bhaskar & George J. Mailath & Stephen Morris, 2009. "A Foundation for Markov Equilibria in Infinite Horizon Perfect Information Games," PIER Working Paper Archive 09-029, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
- Roger Lagunoff & Akihiko Matsu, .
""Asynchronous Choice in Repeated Coordination Games'',"
CARESS Working Papres
96-10, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
- Roger Lagunoff & Akihiko Matsui, 1997. "Asynchronous Choice in Repeated Coordination Games," Econometrica, Econometric Society, vol. 65(6), pages 1467-1478, November.
- Roger Lagunoff & Akihiko Matsui, 1997. "Asynchronous Choice in Repeated Coordination Games," Game Theory and Information 9707002, EconWPA.
- Roger Lagunoff & Akihiko Matsu, . "Asynchronous Choice in Repeated Coordination Games," Penn CARESS Working Papers 23a1aa461811b8f48b0334f6e, Penn Economics Department.
- Hellwig, Martin & Leininger, Wolfgang & Reny, Philip J. & Robson, Arthur J., 1990. "Subgame perfect equilibrium in continuous games of perfect information: An elementary approach to existence and approximation by discrete games," Journal of Economic Theory, Elsevier, vol. 52(2), pages 406-422, December.
- Guilherme Carmona, 2005.
"On Games Of Perfect Information: Equilibria, Ε–Equilibria And Approximation By Simple Games,"
International Game Theory Review (IGTR),
World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 491-499.
- Carmona, Guilherme, 2003. "On Games of Perfect Information: Equilibria, E-Equilibria and Approximation by Simple Games," FEUNL Working Paper Series wp427, Universidade Nova de Lisboa, Faculdade de Economia.
- Doraszelski, Ulrich & Escobar, Juan, 2008.
"A Theory of Regular Markov Perfect Equilibria in Dynamic Stochastic Games: Genericity, Stability, and Purification,"
CEPR Discussion Papers
6805, C.E.P.R. Discussion Papers.
- Doraszelski, Ulrich & Escobar, Juan, 2010. "A theory of regular Markov perfect equilibria in dynamic stochastic games: genericity, stability, and purification," Theoretical Economics, Econometric Society, vol. 5(3), September.
- Juan Escobar & Ulrich Doraszelski, 2008. "A Theory of Regular Markov Perfect Equilibria\\in Dynamic Stochastic Games: Genericity, Stability, and Purification," 2008 Meeting Papers 453, Society for Economic Dynamics.
- Gale, Douglas, 1995.
"Dynamic Coordination Games,"
Springer, vol. 5(1), pages 1-18, January.
- Harris, Christopher J, 1985. "Existence and Characterization of Perfect Equilibrium in Games of Perfect Information," Econometrica, Econometric Society, vol. 53(3), pages 613-28, May.
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