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Differential Games in Industrial Organization

  • Luca Colombo
  • Paola Labrecciosa
Reference work entry

Abstract

In this chapter, we provide an overview of continuous-time games in industrial organization, covering classical papers on adjustment costs, sticky prices, and R&D races, as well as more recent contributions on oligopolistic exploitation of renewable productive assets and strategic investments under uncertainty.

Keywords

Differential oligopoly games Adjustment costs Sticky prices Productive assets Innovation 

References

  1. Azevedo A, Paxson D (2014) Developing real options game models. Eur J Oper Res 237:909–920MathSciNetzbMATHCrossRefGoogle Scholar
  2. Başar T, Olsder GJ (1995) Dynamic noncooperative game theory. Academic Press, San DiegozbMATHGoogle Scholar
  3. Ben Abdelaziz F, Ben Brahim M, Zaccour G (2008) R&D equilibrium strategies with surfers. J Optim Theory Appl 136:1–13MathSciNetzbMATHCrossRefGoogle Scholar
  4. Ben Brahim M, Ben Abdelaziz F, Zaccour G (2016) Strategic investments in R&D and efficiency in the presence of free riders. RAIRO Oper Res 50:611–625MathSciNetzbMATHCrossRefGoogle Scholar
  5. Ben Youssef S, Breton M, Zaccour G (2013) Cooperating and non-cooperating firms in inventive and absorptive research. J Optim Theory Appl 157:229–251MathSciNetzbMATHCrossRefGoogle Scholar
  6. Benchekroun H (2003a) Unilateral production restrictions in a dynamic duopoly. J Econ Theory 111:214–239MathSciNetzbMATHCrossRefGoogle Scholar
  7. Benchekroun H (2003b) The closed-loop effect and the profitability of horizontal mergers. Can J Econ 36:546–565CrossRefGoogle Scholar
  8. Benchekroun H (2008) Comparative dynamics in a productive asset oligopoly. J Econ Theory 138:237–261MathSciNetzbMATHCrossRefGoogle Scholar
  9. Benchekroun H, Gaudet G (2015) On the effects of mergers on equilibrium outcomes in a common property renewable asset oligopoly. J Econ Dyn Control 52:209–223MathSciNetCrossRefGoogle Scholar
  10. Benchekroun H, Gaudet G, Lohoues H (2014) Some effects of asymmetries in a common pool natural resource oligopoly. Strateg Behav Environ 4:213–235CrossRefGoogle Scholar
  11. Benchekroun H, Halsema A, Withagen C (2009) On nonrenewable resource oligopolies: the asymmetric case. J Econ Dyn Control 33:1867–1879MathSciNetzbMATHCrossRefGoogle Scholar
  12. Benchekroun H, Halsema A, Withagen C (2010) When additional resource stocks reduce welfare. J Environ Econ Manag 59:109–114zbMATHCrossRefGoogle Scholar
  13. Benchekroun H, Long NV (2002) Transboundary fishery: a differential game model. Economica 69:207–221CrossRefGoogle Scholar
  14. Benchekroun H, Long NV (2006) The curse of windfall gains in a non-renewable resource oligopoly. Aust Econ Pap 4:99–105CrossRefGoogle Scholar
  15. Benchekroun H, Long NV (2016) Status concern and the exploitation of common pool renewable resources. Ecol Econ 125:70–82CrossRefGoogle Scholar
  16. Benhabib J, Radner R (1992) The joint exploitation of a productive asset: a game theoretic approach. Econ Theory 2:155–190MathSciNetzbMATHCrossRefGoogle Scholar
  17. Besanko D, Doraszelski (2004) Capacity dynamics and endogenous asymmetries in firm size. RAND J Econ 35:23–49Google Scholar
  18. Besanko D, Doraszelski U, Lu LX, Satterthwaite M (2010) On the role of demand and strategic uncertainty in capacity investment and disinvestment dynamics. Int J Ind Organ 28:383–389zbMATHCrossRefGoogle Scholar
  19. Boyer M, Lasserre P, Mariotti T, Moreaux M (2004) Preemption and rent dissipation under price competition. Int J Ind Organ 22:309–328CrossRefGoogle Scholar
  20. Boyer M, Lasserre P, Moreaux M (2012) A dynamic duopoly investment game without commitment under uncertain market expansion. Int J Ind Organ 30:663–681CrossRefGoogle Scholar
  21. Breton M, Turki A, Zaccour G (2004) Dynamic model of R&D, spillovers, and efficiency of Bertrand and Cournot equilibria. J Optim Theory Appl 123:1–25MathSciNetzbMATHCrossRefGoogle Scholar
  22. Breton M, Vencatachellum D, Zaccour G (2006) Dynamic R&D with strategic behavior. Comput Oper Res 33:426–437MathSciNetzbMATHCrossRefGoogle Scholar
  23. Bulow J, Geanakoplos J, Klemperer P (1985) Multimarket oligopoly: strategic substitutes and complements. J Polit Econ 93:488–511CrossRefGoogle Scholar
  24. Cabral L (2012) Oligopoly dynamics. Int J Ind Organ 30:278–282CrossRefGoogle Scholar
  25. Cellini R, Lambertini L (1998) A dynamic model of differentiated oligopoly with capital accumulation. J Econ Theory 83:145–155zbMATHCrossRefGoogle Scholar
  26. Cellini R, Lambertini L (2002) A differential game approach to investment in product differentiation. J Econ Dyn Control 27:51–62MathSciNetzbMATHCrossRefGoogle Scholar
  27. Cellini R, Lambertini L (2004) Dynamic oligopoly with sticky prices: closed-loop, feedback and open-loop solutions. J Dyn Control Syst 10:303–314MathSciNetzbMATHCrossRefGoogle Scholar
  28. Cellini R, Lambertini L (2005) R&D incentives and market structure: a dynamic analysis. J Optim Theory Appl 126:85–96MathSciNetzbMATHCrossRefGoogle Scholar
  29. Cellini R, Lambertini L (2007a) Capital accumulation, mergers, and the Ramsey golden rule. In: Quincampoix M, Vincent T, Jørgensen S (eds) Advances in dynamic game theory and applications. Annals of the international society of dynamic games, vol 8. Birkhäuser, BostonGoogle Scholar
  30. Cellini R, Lambertini L (2007b) A differential oligopoly game with differentiated goods and sticky prices. Eur J Oper Res 176:1131–1144MathSciNetzbMATHCrossRefGoogle Scholar
  31. Cellini R, Lambertini L (2009) Dynamic R&D with spillovers: competition vs cooperation. J Econ Dyn Control 33:568–582MathSciNetzbMATHCrossRefGoogle Scholar
  32. Chang SC, Wu HM (2006) Production experiences and market structure in R&D competition. J Econ Dyn Control 30:163–183MathSciNetzbMATHCrossRefGoogle Scholar
  33. Chevalier-Roignant B, Flath CM, Huchzermeier A, Trigeorgis L (2011) Strategic investment under uncertainty: a synthesis. Eur J Oper Res 215:639–650MathSciNetzbMATHCrossRefGoogle Scholar
  34. Choi JP (1991) Dynamic R&D competition under ‘hazard rate’ uncertainty. RAND J Econ 22: 596–610CrossRefGoogle Scholar
  35. Choi JP (1993) Dynamic R&D competition, research line diversity, and intellectual property rights. J Econ Manag Strateg 2:277–297CrossRefGoogle Scholar
  36. Clemhout S, Wan H Jr (1985) Dynamic common property resources and environmental problems. J Optim Theory Appl 46:471–481MathSciNetzbMATHCrossRefGoogle Scholar
  37. Colombo L, Dawid H (2014) Strategic location choice under dynamic oligopolistic competition and spillovers. J Econ Dyn Control 48:288–307MathSciNetCrossRefGoogle Scholar
  38. Colombo L, Labrecciosa P (2012) Inter-firm knowledge diffusion, market power, and welfare. J Evol Econ 22:1009–1027CrossRefGoogle Scholar
  39. Colombo L, Labrecciosa P (2013a) Oligopoly exploitation of a private property productive asset. J Econ Dyn Control 37:838–853MathSciNetzbMATHCrossRefGoogle Scholar
  40. Colombo L, Labrecciosa P (2013b) On the convergence to the Cournot equilibrium in a productive asset oligopoly. J Math Econ 49:441–445MathSciNetzbMATHCrossRefGoogle Scholar
  41. Colombo L, Labrecciosa P (2015) On the Markovian efficiency of Bertrand and Cournot equilibria. J Econ Theory 155:332–358MathSciNetzbMATHCrossRefGoogle Scholar
  42. D’Aspremont C, Jacquemin A (1988) Cooperative and noncooperative R&D in duopoly with spillovers. Am Econ Rev 78:1133–1137Google Scholar
  43. Dangl T (1999) Investment and capacity choice under uncertain demand. Eur J Oper Res 117: 415–428zbMATHCrossRefGoogle Scholar
  44. Dawid H, Kopel M, Dangl T (2009) Trash it or sell it? A strategic analysis of the market introduction of product innovations. Int Game Theory Rev 11:321–345MathSciNetzbMATHCrossRefGoogle Scholar
  45. Dawid H, Kopel M, Kort PM (2010) Innovation threats and strategic responses in oligopoly markets. J Econ Behav Organ 75:203–222CrossRefGoogle Scholar
  46. Dawid H, Kopel M, Kort PM (2013) R&D competition versus R&D cooperation in oligopolistic markets with evolving structure. Int J Ind Organ 31:527–537CrossRefGoogle Scholar
  47. Dawid H, Keoula MY, Kopel M, Kort PM (2015) Product innovation incentives by an incumbent firm: a dynamic analysis. J Econ Behav Organ 117:411–438CrossRefGoogle Scholar
  48. Decamps JP, Mariotti T, Villeneuve S (2006) Irreversible investments in alternative projects. Econ Theory 28:425–448MathSciNetzbMATHCrossRefGoogle Scholar
  49. Dixit AK, Pindyk R (1994) Investment under uncertainty. Princeton University Press, PrincetonGoogle Scholar
  50. Dockner EJ (1988) On the relation between dynamic oligopolistic competition and long-run competitive equilibrium. Eur J Polit Econ 4:47–64CrossRefGoogle Scholar
  51. Dockner EJ (1992) A dynamic theory of conjectural variations. J Ind Econ 40: 377–395CrossRefGoogle Scholar
  52. Dockner EJ, Feichtinger G, Mehlmann A (1993) Dynamic R&D competition with memory. J Evol Econ 3:145–152CrossRefGoogle Scholar
  53. Dockner EJ, Gaunersdorfer A (2001) On the profitability of horizontal mergers in industries with dynamic competition. Jpn World Econ 13:195–216CrossRefGoogle Scholar
  54. Dockner EJ, Gaunersdorfer A (2002) Dynamic oligopolistic competition and quasi-competitive behavior. In: Zaccour G (ed) Optimal control and differential games – essays in honor of Steffen Jørgensen. Kluwer Academic Publishers, Boston/Dordrecht, pp 107–119Google Scholar
  55. Dockner E, Haug A (1990) Tariffs and quotas under dynamic duopolistic competition. J Int Econ 29:147–159CrossRefGoogle Scholar
  56. Dockner E, Haug A (1991) The closed loop motive for voluntary export restraints. Can J Econ 3:679–685CrossRefGoogle Scholar
  57. Dockner EJ, Jørgensen S, Long NV, Sorger G (2000) Differential games in economics and management science. Cambridge University Press, CambridgezbMATHCrossRefGoogle Scholar
  58. Dockner EJ, Long NV (1993) International pollution control: cooperative versus non-cooperative strategies. J Environ Econ Manag 24:13–29zbMATHCrossRefGoogle Scholar
  59. Dockner EJ, Mosburger G (2007) Capital accumulation, asset values and imperfect product market competition. J Differ Equ Appl 13:197–215MathSciNetzbMATHCrossRefGoogle Scholar
  60. Dockner EJ, Siyahhan B (2015) Value and risk dynamics over the innovation cycle. J Econ Dyn Control 61:1–16MathSciNetCrossRefzbMATHGoogle Scholar
  61. Dockner EJ, Sorger G (1996) Existence and properties of equilibria for a dynamic game on productive assets. J Econ Theory 171:201–227MathSciNetzbMATHGoogle Scholar
  62. Dockner EJ, Wagener FOO (2014) Markov perfect Nash equilibria in models with a single capital stock. Econ Theory 56:585–625MathSciNetzbMATHCrossRefGoogle Scholar
  63. Doraszelski U (2003) An R&D race with knowledge accumulation. RAND J Econ 34:20–42CrossRefGoogle Scholar
  64. Doraszelski U, Pakes A (2007) A framework for applied dynamic analysis in IO. In: Armstrong M, Porter R (eds) Handbook of industrial organization, Elsevier, vol 3, pp 1887–1966Google Scholar
  65. Driskill R (2001) Durable goods oligopoly. Int J Ind Organ 19:391–413CrossRefGoogle Scholar
  66. Driskill R, McCafferty S (1989) Dynamic duopoly with adjustment costs: a differential game approach. J Econ Theory 49:324–338MathSciNetzbMATHCrossRefGoogle Scholar
  67. Driskill R., McCafferty S (1996) Industrial policy and duopolistic trade with dynamic demand. Rev Ind Organ 11:355–373CrossRefGoogle Scholar
  68. Dutta PK, Sundaram RK (1993a) The tragedy of the commons. Econ Theory 3:413–426MathSciNetzbMATHCrossRefGoogle Scholar
  69. Dutta PK, Sundaram RK (1993b) How different can strategic models be? J Econ Theory 60:42–61MathSciNetzbMATHCrossRefGoogle Scholar
  70. El Ouardighi F, Shnaiderman M, Pasin F (2014) Research and development with stock-dependent spillovers and price competition in a duopoly. J Optim Theory Appl 161:626–647MathSciNetzbMATHCrossRefGoogle Scholar
  71. Ericson R, Pakes A (1995) Markov-perfect industry dynamics: a framework for empirical work. Rev Econ Stud 62:53–82zbMATHCrossRefGoogle Scholar
  72. Fershtman C, Kamien M (1987) Dynamic duopolistic competition with sticky prices. Econometrica 55:1151–1164MathSciNetzbMATHCrossRefGoogle Scholar
  73. Fershtman C, Kamien M (1990) Turnpike properties in a finite-horizon differential game: dynamic duopoly with sticky prices. Int Econ Rev 31:49–60MathSciNetzbMATHCrossRefGoogle Scholar
  74. Figuières C (2009) Markov interactions in a class of dynamic games. Theor Decis 66:39–68MathSciNetzbMATHCrossRefGoogle Scholar
  75. Fisher R, Mirman LJ (1992) Strategic dynamic interactions: fish wars. J Econ Dyn Control 16:267–287zbMATHCrossRefGoogle Scholar
  76. Fisher R, Mirman LJ (1996) The complete fish wars: biological and dynamic interactions. J Environ Econ Manag 30:34–42zbMATHCrossRefGoogle Scholar
  77. Friedman JW (1971) A non-cooperative equilibrium for supergames. Rev Econ Stud 28:1–12zbMATHCrossRefGoogle Scholar
  78. Fudenberg D, Tirole J (1985) Preemption and rent equalization in the adoption of new technology. Rev Econ Stud 52:383–401MathSciNetzbMATHCrossRefGoogle Scholar
  79. Fudenberg D, Maskin E (1986) The folk theorem in repeated games with discounting or with incomplete information. Econometrica 54:533–554MathSciNetzbMATHCrossRefGoogle Scholar
  80. Fujiwara K (2008) Duopoly can be more anti-competitive than monopoly. Econ Lett 101: 217–219MathSciNetzbMATHCrossRefGoogle Scholar
  81. Fujiwara K (2009) Gains from trade in a differential game model of asymmetric oligopoly. Rev Int Econ 17:1066–1073CrossRefGoogle Scholar
  82. Fujiwara K (2011) Losses from competition in a dynamic game model of a renewable resource oligopoly. Resour Energy Econ 33:1–11CrossRefGoogle Scholar
  83. Gaudet G, Long NV (1994) On the effects of the distribution of initial endowments in a non-renewable resource duopoly. J Econ Dyn Control 18:1189–1198zbMATHCrossRefGoogle Scholar
  84. Genc T, Reynolds SS, Sen S (2007) Dynamic oligopolistic games under uncertainty: a stochastic programming approach. J Econ Dyn Control 31:55–80MathSciNetzbMATHCrossRefGoogle Scholar
  85. Gilbert R, Harris R (1984) Competition with lumpy investment. RAND J Econ 15:197–212MathSciNetCrossRefGoogle Scholar
  86. Goyal S, Joshi S (2003) Networks of collaboration in oligopoly. Games Econ Behav 43:57–85MathSciNetzbMATHCrossRefGoogle Scholar
  87. Grossman GM, Shapiro C (1987) Dynamic R&D competition. Econ J 97:372–387CrossRefGoogle Scholar
  88. Gutiérrez O, Ruiz-Aliseda F (2011) Real options with unknown-date events. Ann Finance 7:171–198MathSciNetzbMATHCrossRefGoogle Scholar
  89. Hamermesh D, Pfann G (1996) Adjustment costs in factor demand. J Econ Lit 34:1264–1292Google Scholar
  90. Haurie A, Krawczyk JB, Zaccour G (2012) Games and dynamic games. World Scientific, SingaporezbMATHCrossRefGoogle Scholar
  91. Haurie A, Zaccour G (2005) S-adapted equilibria in games played over event trees: an overview. Ann Int Soc Dyn Games 7:367–400zbMATHGoogle Scholar
  92. Huberts NFD., Huisman KJM, Kort PM, Lavrutich MN (2015) Capacity choice in (strategic) real options models: a survey. Dyn Games Appl 5:424–439MathSciNetzbMATHCrossRefGoogle Scholar
  93. Huisman K, Kort P (2004) Strategic technology adoption taking into account future technological improvements: a real options approach. Eur J Oper Res 159:705–728MathSciNetzbMATHCrossRefGoogle Scholar
  94. Huisman K, Kort P (2015) Strategic capacity investment under uncertainty. RAND J Econ 46: 376–408CrossRefGoogle Scholar
  95. Janssens G, Zaccour G (2014) Strategic price subsidies for new technologies. Automatica 50: 1999–2006MathSciNetzbMATHCrossRefGoogle Scholar
  96. Jørgensen S, Yeung DWK (1996) Stochastic differential game model of common property fishery. J Optim Theory Appl 90:381–403MathSciNetzbMATHCrossRefGoogle Scholar
  97. Jørgensen S, Zaccour G (2004) Differential games in marketing. Dordrecht, KluwerCrossRefGoogle Scholar
  98. Jørgensen S, Zaccour G (2014) A survey of game-theoretic models of cooperative advertising. Eur J Oper Res 237:1–14MathSciNetzbMATHCrossRefGoogle Scholar
  99. Judd K (1998) Numerical methods in economics. MIT Press, CambridgezbMATHGoogle Scholar
  100. Jun B, Vives X (2004) Strategic incentives in dynamic duopoly. J Econ Theory 116:249–281MathSciNetzbMATHCrossRefGoogle Scholar
  101. Kamien MI, Muller E, Zang I (1992) Cooperative joint ventures and R&D cartels. Am Econ Rev 82:1293–1306Google Scholar
  102. Kamien MI, Zang I (2000) Meet me half way: research joint ventures and absorptive capacity. Int J Ind Organ 18:995–1012CrossRefGoogle Scholar
  103. Karp L (1992a) Efficiency inducing tax for a common property oligopoly. Econ J 102:321–332CrossRefGoogle Scholar
  104. Karp L (1992b) Social welfare in a common property oligopoly. Int Econ Rev 33:353–372zbMATHCrossRefGoogle Scholar
  105. Karp L, Perloff J (1989) Dynamic oligopoly in the rice export market. Rev Econ Stat 71:462–470CrossRefGoogle Scholar
  106. Karp L, Perloff J (1993a) Open-loop and feedback models of dynamic oligopoly. Int J Ind Organ 11:369–389CrossRefGoogle Scholar
  107. Karp L, Perloff J (1993b) A dynamic model of oligopoly in the coffee export market. Am J Agric Econ 75:448–457CrossRefGoogle Scholar
  108. Kobayashi S (2015) On a dynamic model of cooperative and noncooperative R&D oligopoly with spillovers. Dyn Games Appl 5:599–619MathSciNetzbMATHCrossRefGoogle Scholar
  109. Lambertini L, Mantovani A (2014) Feedback equilibria in a dynamic renewable resource oligopoly: pre-emption, voracity and exhaustion. J Econ Dyn Control 47:115–122MathSciNetCrossRefGoogle Scholar
  110. Levhari D, Mirman L (1980) The great fish war: an example using a dynamic Cournot-Nash solution. Bell J Econ 11:322–334MathSciNetzbMATHCrossRefGoogle Scholar
  111. Lewis T, Schmalensee R (1980) Cartel and oligopoly pricing of non-replenishable natural resources. In: Liu P (ed) Dynamic optimization and application to economics. Plenum Press, New YorkzbMATHGoogle Scholar
  112. Long NV (2010) A survey of dynamic games in economics. World Scientific, SingaporezbMATHCrossRefGoogle Scholar
  113. Long NV (2015) Dynamic games between firms and infinitely lived consumers: a review of the literature. Dyn Games Appl 5:467–492MathSciNetzbMATHCrossRefGoogle Scholar
  114. Loury G (1986) A theory of ‘oil’igopoly: Cournot equilibrium in exhaustible resource market with fixed supplies. Int Econ Rev 27:285–301MathSciNetzbMATHCrossRefGoogle Scholar
  115. Malueg DA, Tsutsui SO (1997) Dynamic R&D competition with learning. RAND J Econ 28:751–772CrossRefGoogle Scholar
  116. Maskin E, Tirole J (2001) Markov perfect equilibrium I. Observable actions. J Econ Theory 100:191–219MathSciNetzbMATHCrossRefGoogle Scholar
  117. Mehlmann A, Willing R (1983) On non-unique closed-loop Nash equilibria for a class of differential games with a unique and degenerated feedback solution. J Optim Theory Appl 41:463–472MathSciNetzbMATHCrossRefGoogle Scholar
  118. Murto P (2004) Exit in duopoly under uncertainty. RAND J Econ 35:111–127CrossRefGoogle Scholar
  119. Navas J, Kort PM (2007) Time to complete and research joint ventures: a differential game approach. J Econ Dyn Control 31:1672–1696MathSciNetzbMATHCrossRefGoogle Scholar
  120. Okuguchi K (1973) Quasi-competitiveness and Cournot oligopoly. Rev Econ Stud 40:145–148CrossRefGoogle Scholar
  121. Pawlina G, Kort P (2006) Real options in an asymmetric duopoly: who benefits from your competitive disadvantage? J Econ Manag Strateg 15:1–35CrossRefGoogle Scholar
  122. Petit ML, Tolwinski B (1996) Technology sharing cartels and industrial structure. Int J Ind Organ 15:77–101CrossRefGoogle Scholar
  123. Petit ML, Tolwinski B (1999) R&D cooperation or competition? Eur Econ Rev 43:185–208CrossRefGoogle Scholar
  124. Qiu L (1997) On the dynamic efficiency of Bertrand and Cournot equilibria. J Econ Theory 75:213–229MathSciNetzbMATHCrossRefGoogle Scholar
  125. Ramsey FP (1928) A mathematical theory of saving. Econ J 38:543–559CrossRefGoogle Scholar
  126. Reinganum J (1981) Dynamic games of innovation. J Econ Theory 25:21–41MathSciNetzbMATHCrossRefGoogle Scholar
  127. Reinganum J (1982) A dynamic game of R&D: patent protection and competitive behavior. Econometrica 50:671–688MathSciNetzbMATHCrossRefGoogle Scholar
  128. Reinganum J, Stokey N (1985) Oligopoly extraction of a common property resource: the importance of the period of commitment in dynamic games. Int Econ Rev 26:161–173MathSciNetzbMATHCrossRefGoogle Scholar
  129. Reynolds S (1987) Capacity investment, preemption and commitment in an infinite horizon model. Int Econ Rev 28:69–88MathSciNetzbMATHCrossRefGoogle Scholar
  130. Reynolds S (1991) Dynamic oligopoly with capacity adjustment costs. J Econ Dyn Control 15:491–514MathSciNetzbMATHCrossRefGoogle Scholar
  131. Rincón-Zapatero J, Martinez J, Martín-Herrán G (1998) New method to characterize subgame perfect Nash equilibria in differential games. J Optim Theory Appl 96:377–395MathSciNetzbMATHCrossRefGoogle Scholar
  132. Roos CF (1925) A mathematical theory of competition. Am J Mathem 46:163–175MathSciNetzbMATHCrossRefGoogle Scholar
  133. Roos CF (1927) A Dynamical theory of economics. J Polit Econ 35:632–656CrossRefGoogle Scholar
  134. Ruffin RJ (1971) Cournot oligopoly and competitive behaviour. Rev Econ Stud 38:493–502zbMATHCrossRefGoogle Scholar
  135. Ruiz-Aliseda F, Wu J (2012) Irreversible investments in stochastically cyclical markets. J Econ Manag Strateg 21:801–847CrossRefGoogle Scholar
  136. Ruiz-Aliseda F (2016) Preemptive investments under uncertainty, credibility, and first mover advantages. Int J Ind Organ 44:123–137CrossRefGoogle Scholar
  137. Salant SW, Shaffer G (1998) Optimal asymmetric strategies in research joint ventures. Int J Ind Organ 16:195–208CrossRefGoogle Scholar
  138. Salant SW, Switzer S, Reynolds R (1983) Losses from horizontal merger: the effects of an exogenous change in industry structure on Cournot-Nash equilibrium. Q J Econ 98:185–213CrossRefGoogle Scholar
  139. Simaan M, Takayama T (1978) Game theory applied to dynamic duopoly problems with production constraints. Automatica 14:161–166zbMATHCrossRefGoogle Scholar
  140. Simon LK, Stinchcombe MB (1989) Extensive form games in continuous time: pure strategies. Econometrica 57:1171–1214MathSciNetzbMATHCrossRefGoogle Scholar
  141. Singh N, Vives X (1984) Price and quantity competition in a differentiated duopoly. RAND J Econ 15:546–554CrossRefGoogle Scholar
  142. Symeonidis G (2003) Comparing Cournot and Bertrand equilibria in a differentiated duopoly with product R&D. Int J Ind Organ 21:39–55CrossRefGoogle Scholar
  143. Sorger G (2005) A dynamic common property resource problem with amenity value and extraction costs. Int J Econ Theory 1:3–19CrossRefGoogle Scholar
  144. Spence M (1977) Entry, capacity, investment and oligopolistic pricing. Bell J Econ 8:534–544CrossRefGoogle Scholar
  145. Spence M (1979) Investment strategy and growth in a new market. Bell J Econ 10:1–19CrossRefGoogle Scholar
  146. Thijssen J, Huisman K, Kort PM (2012) Symmetric equilibrium strategies in game theoretic real option models. J Math Econ 48:219–225MathSciNetzbMATHCrossRefGoogle Scholar
  147. Tsutsui S (1996) Capacity constraints and voluntary output cutback in dynamic Cournot competition. J Econ Dyn Control 20:1683–1708MathSciNetzbMATHCrossRefGoogle Scholar
  148. Tsutsui S, Mino K (1990) Nonlinear strategies in dynamic duopolistic competition with sticky prices. J Econ Theory 52:136–161MathSciNetzbMATHCrossRefGoogle Scholar
  149. Vencatachellum D (1998) A differential R&D game: implications for knowledge-based growth models. J Optim Theory Appl 96:175–189MathSciNetzbMATHCrossRefGoogle Scholar
  150. Vives X (1999) Oligopoly pricing: old ideas and new tools, 1st edn, vol 1. MIT Press Books/The MIT Press, CambridgeGoogle Scholar
  151. Weeds H (2002) Strategic delay in a real options model of R&D competition. Rev Econ Stud 69:729–747MathSciNetzbMATHCrossRefGoogle Scholar
  152. Wirl F (2010) Dynamic demand and noncompetitive intertemporal output adjustments. Int J Ind Organ 28:220–229CrossRefGoogle Scholar
  153. Wirl F, Dockner EJ (1995) Leviathan governments and carbon taxes: costs and potential benefits. Eur Econ Rev 39:1215–1236CrossRefGoogle Scholar
  154. Wirl F (1996) Dynamic voluntary provision of public goods: extension to nonlinear strategies. Eur J Polit Econ 12:555–560CrossRefGoogle Scholar
  155. Wiszniewska-Matyszkiel A, Bodnar M, Mirota F (2015) Dynamic oligopoly with sticky prices: off-steady-state analysis. Dyn Games Appl 5:568–598MathSciNetzbMATHCrossRefGoogle Scholar
  156. Yang M, Zhou Q (2007) Real options analysis for efficiency of entry deterrence with excess capacity. Syst Eng Theory Pract (27):63–70CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of EconomicsDeakin UniversityBurwoodAustralia
  2. 2.Department of EconomicsMonash UniversityClaytonAustralia

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