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Industry dynamics: Foundations for models with an infinite number of firms

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  • Weintraub, Gabriel Y.
  • Benkard, C. Lanier
  • Van Roy, Benjamin

Abstract

This paper explores the connection between three important threads of economic research offering different approaches to studying the dynamics of an industry with heterogeneous firms. Finite models of the form pioneered by Ericson and Pakes (1995) capture the dynamics of a finite number of heterogeneous firms as they compete in an industry, and are typically analyzed using the concept of Markov perfect equilibrium (MPE). Infinite models of the form pioneered by Hopenhayn (1992), on the other hand, consider an infinite number of infinitesimal firms, and are typically analyzed using the concept of stationary equilibrium (SE). A third approach uses oblivious equilibrium (OE), which maintains the simplifying benefits of an infinite model but within the more realistic setting of a finite model. The paper relates these three approaches. The main result of the paper provides conditions under which SE of infinite models approximate MPE of finite models arbitrarily well in asymptotically large markets. Our conditions require that the distribution of firm states in SE obeys a certain âlight-tailâ condition. In a second set of results, we show that the set of OE of a finite model approaches the set of SE of the infinite model in large markets under a similar light-tail condition.

Suggested Citation

  • Weintraub, Gabriel Y. & Benkard, C. Lanier & Van Roy, Benjamin, 2011. "Industry dynamics: Foundations for models with an infinite number of firms," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1965-1994, September.
  • Handle: RePEc:eee:jetheo:v:146:y:2011:i:5:p:1965-1994
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    References listed on IDEAS

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    Cited by:

    1. repec:spr:joptap:v:166:y:2015:i:2:d:10.1007_s10957-014-0649-9 is not listed on IDEAS
    2. Régis Chenavaz & Corina Paraschiv & Gabriel Turinici, 2017. "Dynamic Pricing of New Products in Competitive Markets: A Mean-Field Game Approach," Working Papers hal-01592958, HAL.
    3. repec:spr:jogath:v:46:y:2017:i:2:d:10.1007_s00182-016-0539-5 is not listed on IDEAS
    4. Adlakha, Sachin & Johari, Ramesh & Weintraub, Gabriel Y., 2015. "Equilibria of dynamic games with many players: Existence, approximation, and market structure," Journal of Economic Theory, Elsevier, vol. 156(C), pages 269-316.
    5. Jian Yang, 2015. "A Link between Sequential Semi-anonymous Nonatomic Games and their Large Finite Counterparts," Papers 1510.06809, arXiv.org, revised Jun 2016.
    6. Jian Yang, 2015. "Analysis of Markovian Competitive Situations using Nonatomic Games," Papers 1510.06813, arXiv.org, revised Apr 2017.

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