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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).

Suggested Citation

  • Marcel Boyer & Pierre Lasserre & Michel Moreaux, 2011. "A Dynamic Duopoly Investment Game without Commitment under Uncertain Market Expansion," CIRANO Working Papers 2011s-65, CIRANO.
  • Handle: RePEc:cir:cirwor:2011s-65
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    Cited by:

    1. Kuno J.M. Huisman & Peter M. Kort, 2015. "Strategic capacity investment under uncertainty," RAND Journal of Economics, RAND Corporation, pages 376-408.
    2. Azevedo, Alcino & Paxson, Dean, 2014. "Developing real option game models," European Journal of Operational Research, Elsevier, pages 909-920.
    3. Richard Ruble & Bruno Versaevel, 2012. "On the tacit collusion equilibria of a dynamic duopoly investment game," Economics Bulletin, AccessEcon, pages 2817-2827.
    4. Billette de Villemeur, Etienne & Ruble, Richard & Versaevel, Bruno, 2014. "Innovation and imitation incentives in dynamic duopoly," MPRA Paper 59453, University Library of Munich, Germany.
    5. Nishide, Katsumasa & Yagi, Kyoko, 2016. "Investment under regime uncertainty: Impact of competition and preemption," International Journal of Industrial Organization, Elsevier, pages 47-58.
    6. Bruno Versaevel, 2015. "Alertness, Leadership, and Nascent Market Dynamics," Dynamic Games and Applications, Springer, pages 440-466.
    7. Ruiz-Aliseda, Francisco, 2016. "Preemptive investments under uncertainty, credibility and first mover advantages," International Journal of Industrial Organization, Elsevier, pages 123-137.
    8. Kuno J.M. Huisman & Peter M. Kort, 2015. "Strategic capacity investment under uncertainty," RAND Journal of Economics, RAND Corporation, pages 376-408.
    9. Arasteh, Abdollah, 2017. "Considering the investment decisions with real options games approach," Renewable and Sustainable Energy Reviews, Elsevier, pages 1282-1294.
    10. Allain, Marie-Laure & Boyer, Marcel & Kotchoni, Rachidi & Ponssard, Jean-Pierre, 2015. "Are cartel fines optimal? Theory and evidence from the European Union," International Review of Law and Economics, Elsevier, pages 38-47.
    11. Richard Ruble & Bruno Versaevel, 2012. "On the tacit collusion equilibria of a dynamic duopoly investment game," Economics Bulletin, AccessEcon, pages 2817-2827.
    12. Lavrutich, Maria N. & Huisman, Kuno J.M. & Kort, Peter M., 2016. "Entry deterrence and hidden competition," Journal of Economic Dynamics and Control, Elsevier, pages 409-435.
    13. Billette de Villemeur, Etienne & Ruble, Richard & Versaevel, Bruno, 2014. "Investment timing and vertical relationships," International Journal of Industrial Organization, Elsevier, pages 110-123.
    14. 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.
    15. Billette de Villemeur, Etienne & Ruble, Richard & Versaevel, Bruno, 2015. "On the timing of innovation and imitation," MPRA Paper 69161, University Library of Munich, Germany.
    16. Etienne Billette de Villemeur & Richard Ruble & Bruno Versaevel, 2011. "Coordination and Cooperation in Investment Timing with Externalities?," Working Papers 1128, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    17. 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.
    18. Billette de Villemeur, Etienne & Ruble, Richard & Versaevel, Bruno, 2014. "Investment timing and vertical relationships," International Journal of Industrial Organization, Elsevier, pages 110-123.
    19. repec:eee:dyncon:v:84:y:2017:i:c:p:1-31 is not listed on IDEAS
    20. de Villemeur, Etienne Billette & Ruble, Richard & Versaevel, Bruno, 2013. "Caveat preemptor: Coordination failure and success in a duopoly investment game," Economics Letters, Elsevier, pages 250-254.
    21. de Villemeur, Etienne Billette & Ruble, Richard & Versaevel, Bruno, 2013. "Caveat preemptor: Coordination failure and success in a duopoly investment game," Economics Letters, Elsevier, pages 250-254.
    22. Billette de Villemeur, Etienne & Ruble, Richard & Versaevel, Bruno, 2016. "When should a winner take all, or pay some? Innovation and imitation incentives in a dynamic duopoly," MPRA Paper 75465, University Library of Munich, Germany.

    More about this item

    Keywords

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

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D92 - Microeconomics - - Micro-Based Behavioral Economics - - - Intertemporal Firm Choice, Investment, Capacity, and Financing
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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