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Equilibrium analysis of dynamic models of imperfect competition

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  • Escobar, Juan F.

Abstract

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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    Cited by:

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    2. Dawid, Herbert & Keoula, Michel Y. & Kopel, Michael & Kort, Peter M., 2023. "Dynamic investment strategies and leadership in product innovation," European Journal of Operational Research, Elsevier, vol. 306(1), pages 431-447.
    3. Marc Bourreau & Yutec Sun, 2022. "Competition and Quality: Evidence from the Entry of Mobile Network Service," Working Papers 22-04, NET Institute.
    4. Jenkins, Mark & Liu, Paul & Matzkin, Rosa L. & McFadden, Daniel L., 2021. "The browser war — Analysis of Markov Perfect Equilibrium in markets with dynamic demand effects," Journal of Econometrics, Elsevier, vol. 222(1), pages 244-260.
    5. Arthur Charpentier & Romuald Élie & Carl Remlinger, 2023. "Reinforcement Learning in Economics and Finance," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 425-462, June.

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    More about this item

    Keywords

    Industry dynamics; Dynamic stochastic games; Markov perfect equilibrium;
    All these keywords.

    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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