Journal of Evolutionary Economics

, Volume 27, Issue 5, pp 877–903 | Cite as

Evolutionary dynamics of a duopoly game with strategic delegation and isoelastic demand

Regular Article


We analyze a model of strategic delegation in Cournot competition with isoelastic demand. We first consider the static game and then we address an evolutionary version of it. We show that the result for which under quantity competition strategic delegation entails output expansion and higher consumers’ welfare than at the standard Cournot-Nash equilibrium is not necessarily true, but depends on the price elasticity of demand. Then, we study the main welfare implications of the model in order to understand whether the prevailing long-run industry configuration provides the highest welfare. We show that this may occur when both firms provide a mixed incentive and that, in this case, the model admits feasible trajectories the long-run configuration of which yields the highest welfare. Finally, we address the robustness of our results by means of an evolutionary model with heterogeneous players.


Strategic delegation Evolutionary games Quantity competition Isoelastic demand Cartel stability 

JEL Classification

C73 L13 L21 D43 



The authors would like to thank Mario Pezzino and Davide Radi as well as the anonymous referees for helpful comments on the paper. The usual disclaimer applies. Fabio Lamantia gratefully acknowledges financial support from EU COST Action IS1104 The EU in the new economic complex geography: models, tools and policy evaluation. This work is part of the research project Dynamic models for behavioral economics, DESP - University of Urbino, Italy.


  1. Agliari A, Gardini L, Puu T (2006) Global bifurcations in duopoly when the Cournot point is destabilized via a subcritical Neimark bifurcation. Int Game Theory Rev 8(1):1–20CrossRefGoogle Scholar
  2. Alger I, Weibull J (2013) Homo moralis - preference evolution under incomplete information and assortative matching. Econometrica 81(6):2269–2302CrossRefGoogle Scholar
  3. Basu K (1995) Stackelberg equilibrium in oligopoly: an explanation based on managerial incentives. Econ Lett, pp. 459–464Google Scholar
  4. Beard R (2015) N-firm oligopoly with general iso-elastic demand. Bull Econ Res 67(4):336–345CrossRefGoogle Scholar
  5. Bischi GI, Chiarella C, Kopel M, Szidarovszky F (2010) Nonlinear Oligopolies: Stability and Bifurcation. SpringerGoogle Scholar
  6. Bischi GI, Lamantia F, Radi D (2015) An evolutionary Cournot model with limited market knowledge. J Econ Behav Organ 116:219–238CrossRefGoogle Scholar
  7. Bischi GI, Naimzada AK, Sbragia L (2007) Oligopoly games with local monopolistic approximation. J Econ Behav Organ 62(3):371–388CrossRefGoogle Scholar
  8. Cabrales A, Sobel J (1992) On the limit points of discrete selection dynamics. J Econ Theory 57:407–419CrossRefGoogle Scholar
  9. Cerboni Baiardi L, Lamantia F, Radi D (2015) Evolutionary competition between boundedly rational behavioral rules in oligopoly games. Chaos Solitons Fract 79:204–225CrossRefGoogle Scholar
  10. Cressman R (2003) Evolutionary dynamics and extensive form games. The MIT Press, CambridgeGoogle Scholar
  11. d’Aspremont C, Jacquemin A, Gabszewicz J, Weymark J (1983) On the stability of collusive price leadership. Can J Econ 16(1):17–25CrossRefGoogle Scholar
  12. De Giovanni D, Lamantia F (2016) Control delegation, information and beliefs in evolutionary oligopolies. J Evol Econ 26(5):1089–1116CrossRefGoogle Scholar
  13. Droste E, Hommes C, Tuinstra J (2002) Endogenous fluctuations under evolutionary pressure in Cournot competition. Games Econ Behav 40:232–269CrossRefGoogle Scholar
  14. Fershtman C, Judd KL (1987) Equilibrium incentives in oligopoly. Am Econ Rev 77(5):926–940Google Scholar
  15. Friedman D, Ostrov DN (2010) Gradient dynamics in population games: some basic results. J Math Econ 46(5):691–707CrossRefGoogle Scholar
  16. Friedman D, Ostrov DN (2013) Evolutionary dynamics over continuous action space for population games that arise from symmetric two–player games. J Econ Theory 148:743–777CrossRefGoogle Scholar
  17. Heifetz A, Shannon C, Spiegel Y (2007) What to maximize if you must. J Econ Theory 133(1):31–57CrossRefGoogle Scholar
  18. Hofbauer J, Weibull J (1996) Evolutionary selection against dominated strategies. J Econ Theory 71:558–573CrossRefGoogle Scholar
  19. Koċkesen L (2007) Unobservable contracts as precommitments. Econ Theory 31:539–552CrossRefGoogle Scholar
  20. Königstein M, Müller W (2001) Why firms should care for customers. Econ Lett 72(1):47–52CrossRefGoogle Scholar
  21. Kopel M, Lamantia F, Szidarovszky F (2014) Evolutionary competition in a mixed market with socially concerned firms. J Econ Dyn Control 48:394–409CrossRefGoogle Scholar
  22. Kopel M, Pezzino M (2016) Strategic delegation in oligopoly. In: Corchón LC, Marini MA (eds) Handbook of Game Theory and Industrial Organization. Elgar PublishingGoogle Scholar
  23. Lamantia F (2011) A nonlinear duopoly with efficient production-capacity levels. Comput Econ 38(3):295–309CrossRefGoogle Scholar
  24. Lambertini L (2010) Oligopoly with hyperbolic demand: a differential game approach. J Optim Theory Appl 145:108–119CrossRefGoogle Scholar
  25. Le Veque RJ (2005) Numerical methods for conservation laws. Basel, Birkhäuser VerlagGoogle Scholar
  26. Oechssler J, Riedel F (2001) Evolutionary dynamics on infinite strategy spaces. Econ Theory 17(1):141–162CrossRefGoogle Scholar
  27. Puu T (1991) Chaos in duopoly pricing. Chaos Solitons Fract 1(6):573–581CrossRefGoogle Scholar
  28. Rabanal JP (2017) On the evolution of continuous types under replicator and gradient dynamics: two examples. Dyn Games Appl 7(1):76–92CrossRefGoogle Scholar
  29. Schaffer ME (1989) Are profit-maximizers the best survivors? J Econ Behav Organ 12:29–45CrossRefGoogle Scholar
  30. Sklivas SD (1987) The strategic choice of managerial incentives. RAND J Econ 18(3):452–458CrossRefGoogle Scholar
  31. Vickers J (1985) Delegation and the theory of the firm. Econ J 95(S):138–147CrossRefGoogle Scholar
  32. Weibull J (1985) Evolutionary game theory. The MIT Press, CambridgeGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Economics, Statistics and FinanceUniversity of CalabriaRendeItaly
  2. 2.School of Social SciencesUniversity of ManchesterManchesterUK

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