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A Dynamic Duopoly Investment Game without Commitment under Uncertain Market Expansion

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  • Marcel Boyer

    ()

  • Pierre Lasserre

    ()

  • Michel Moreaux

    ()

Abstract

We model capacity-building investments in a homogeneous product duopoly facing uncertain demand growth. Capacity building is achieved through the addition of production units that are durable and lumpy and whose cost is irreversible. While building their capacity over time, firms compete à la Cournot in the product market given their installed capacity. There is no exogenous order of moves, no commitment regarding future decisions, and no finite horizon. We investigate Markov Perfect Equilibrium (MPE) paths of the investment game, which may include episodes during which firms invest at different times, a preemption pattern, and episodes in which firms invest simultaneously, a tacit collusion pattern. These episodes may alternate and are typically several. When firms have yet to invest in capacity, the sole pattern that is MPE-compatible is a preemption episode: firms invest at different times but have equal value. The first such investment may occur earlier and therefore be riskier than socially optimal. When both firms hold capacity, tacit collusion episodes may be MPE-compatible: firms invest simultaneously at a postponed time (hence holding back production in the meantime), thereby generating an investment wave in the industry. Such investment episodes are more likely with higher demand volatility, faster market growth, and lower cost of capital (discount rate).

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 2011s-65.

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Date of creation: 01 Oct 2011
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Handle: RePEc:cir:cirwor:2011s-65

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Keywords: Real Options; Dynamic Duopoly; Lumpy Investments; Preemption; Investment Waves; Tacit Collusion;

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Citations

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Cited by:
  1. Marie-Laure Allain & Marcel Boyer & Rachidi Kotchoni & Jean-Pierre Ponssard, 2011. "The Determination of Optimal Fines in Cartel Cases The Myth of Underdeterrence," Working Papers hal-00631432, HAL.
  2. Azevedo, Alcino & Paxson, Dean, 2014. "Developing real option game models," European Journal of Operational Research, Elsevier, vol. 237(3), pages 909-920.
  3. Etienne Billette De Villemeur & Richard Ruble & Bruno Versaevel, 2011. "Coordination and Cooperation in Investment Timing with Externalities ?," Post-Print halshs-00639471, HAL.
  4. Thomas Fagart, 2014. "Markovian Equilibrium in a Model of Investment Under Imperfect Competition," Documents de travail du Centre d'Economie de la Sorbonne 14039, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  5. Thomas Fagart, 2014. "Markovian Equilibrium in a Model of Investment Under Imperfect Competition," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01020398, HAL.
  6. Billette de Villemeur, Etienne & Ruble, Richard & Versaevel, Bruno, 2013. "Investment Timing and Vertical Relationships," MPRA Paper 47804, University Library of Munich, Germany.
  7. Richard Ruble & Bruno Versaevel, 2012. "On the tacit collusion equilibria of a dynamic duopoly investment game," Economics Bulletin, AccessEcon, vol. 32(4), pages 2817-2827.
  8. Marie-Laure Allain & Marcel Boyer & Rachidi Kotchoni & Jean-Pierre Ponssard, 2013. "Are Cartel Fines Optimal? Theory and Evidence from the European Union," CIRANO Working Papers 2013s-24, CIRANO.
  9. de Villemeur, Etienne Billette & Ruble, Richard & Versaevel, Bruno, 2013. "Caveat preemptor: Coordination failure and success in a duopoly investment game," Economics Letters, Elsevier, vol. 118(2), pages 250-254.
  10. Huisman, K.J.M. & Kort, P.M., 2013. "Strategic Capacity Investment Under uncertainty," Discussion Paper 2013-003, Tilburg University, Center for Economic Research.

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