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Equilibrium analysis of dynamic models of imperfect competition

  • Escobar, Juan F.

Motivated by recent developments in applied dynamic analysis, this paper presents new sufficient conditions for the existence of a Markov perfect equilibrium in dynamic stochastic games. The main results imply the existence of a Markov perfect equilibrium provided the sets of actions are compact, the set of states is countable, the period payoff functions are upper semi-continuous in action profiles and lower semi-continuous in actions taken by rival firms, and the transition function depends continuously on actions. Moreover, if for each firm a static best-reply set is convex, the equilibrium can be taken in pure strategies. We present and discuss sufficient conditions for the convexity of the best replies. In particular, we introduce new sufficient conditions that ensure the dynamic programming problem each firm faces has a convex solution set, and deduce the existence of a Markov perfect equilibrium for this class of games. Our results expand and unify the available modeling alternatives and apply to several models of interest in industrial organization, including models of industry dynamics.

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Article provided by Elsevier in its journal International Journal of Industrial Organization.

Volume (Year): 31 (2013)
Issue (Month): 1 ()
Pages: 92-101

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Handle: RePEc:eee:indorg:v:31:y:2013:i:1:p:92-101
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505551

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  1. Bajari, Patrick & Benkard, C. Lanier & Levin, Jonathan, 2007. "Estimating Dynamic Models of Imperfect Competition," Research Papers 1852r1, Stanford University, Graduate School of Business.
  2. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
  3. Horst, Ulrich, 2005. "Stationary equilibria in discounted stochastic games with weakly interacting players," Games and Economic Behavior, Elsevier, vol. 51(1), pages 83-108, April.
  4. 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.
  5. Bernheim, B. Douglas & Ray, Debraj, 1989. "Markov perfect equilibria in altruistic growth economies with production uncertainty," Journal of Economic Theory, Elsevier, vol. 47(1), pages 195-202, February.
  6. Ericson, Richard & Pakes, Ariel, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," Review of Economic Studies, Wiley Blackwell, vol. 62(1), pages 53-82, January.
  7. Amir, Rabah, 1996. "Continuous Stochastic Games of Capital Accumulation with Convex Transitions," Games and Economic Behavior, Elsevier, vol. 15(2), pages 111-131, August.
  8. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, March.
  9. Ulrich Doraszelski & Mark Satterthwaite, 2010. "Computable Markov-perfect industry dynamics," RAND Journal of Economics, RAND Corporation, vol. 41(2), pages 215-243.
  10. Curtat, Laurent O., 1996. "Markov Equilibria of Stochastic Games with Complementarities," Games and Economic Behavior, Elsevier, vol. 17(2), pages 177-199, December.
  11. Dutta, Prajit K & Sundaram, Rangarajan, 1992. "Markovian Equilibrium in a Class of Stochastic Games: Existence Theorems for Discounted and Undiscounted Models," Economic Theory, Springer, vol. 2(2), pages 197-214, April.
  12. repec:spr:compst:v:66:y:2007:i:3:p:513-530 is not listed on IDEAS
  13. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-81, July.
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