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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.

Suggested Citation

  • Escobar, Juan F., 2013. "Equilibrium analysis of dynamic models of imperfect competition," International Journal of Industrial Organization, Elsevier, vol. 31(1), pages 92-101.
  • Handle: RePEc:eee:indorg:v:31:y:2013:i:1:p:92-101 DOI: 10.1016/j.ijindorg.2012.10.005

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    References listed on IDEAS

    1. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-781, July.
    2. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
    3. 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.
    4. Ulrich Doraszelski & Mark Satterthwaite, 2010. "Computable Markov-perfect industry dynamics," RAND Journal of Economics, RAND Corporation, vol. 41(2), pages 215-243.
    5. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, June.
    6. Amir, Rabah, 1996. "Continuous Stochastic Games of Capital Accumulation with Convex Transitions," Games and Economic Behavior, Elsevier, vol. 15(2), pages 111-131, August.
    7. Richard Ericson & Ariel Pakes, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," Review of Economic Studies, Oxford University Press, vol. 62(1), pages 53-82.
    8. Dutta, Prajit K & Sundaram, Rangarajan, 1992. "Markovian Equilibrium in a Class of Stochastic Games: Existence Theorems for Discounted and Undiscounted Models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(2), pages 197-214, April.
    9. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
    10. repec:spr:compst:v:66:y:2007:i:3:p:513-530 is not listed on IDEAS
    11. 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.
    12. Curtat, Laurent O., 1996. "Markov Equilibria of Stochastic Games with Complementarities," Games and Economic Behavior, Elsevier, vol. 17(2), pages 177-199, December.
    13. 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.
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    More about this item


    Industry dynamics; Dynamic stochastic games; Markov perfect equilibrium;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium


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