# American Institute of Mathematical Sciences

July 2018, 5(3): 231-242. doi: 10.3934/jdg.2018015

## Strategic delegation effects on Cournot and Stackelberg competition

 University of Piraeus, Economics Department, 80 Karaoli & Dimitriou Strs., 185 34, Greece

Received  January 2018 Revised  March 2018 Published  July 2018

This paper compares the outcomes of two three-stage games of two firms competing for quantity with managerial delegation. In fact, we prove that simultaneous choice of managers by the proprietors of the firms followed by Stackelberg-type competition is equivalent to sequential choice of managers followed by Cournot-type competition. We prove equivalence in a general setting, namely, when the duopolistic model is characterised by a non-linear inverse demand function of the form $p_i = a-(q_i)^n-γ (q_j)^n$, $i,j = 1,2$ and $n∈\mathbb{N}$.

Citation: Nickolas J. Michelacakis. Strategic delegation effects on Cournot and Stackelberg competition. Journal of Dynamics & Games, 2018, 5 (3) : 231-242. doi: 10.3934/jdg.2018015
##### References:
 [1] C. Fershtman and K. L. Judd, Equilibrium incentives in oligopoly, American Economic Review, 77 (1987), 927-940. [2] E. Gal-Or, First mover and second mover advantages, International Economic Review, 26 (1985), 649-653. doi: 10.2307/2526710. [3] M. Kopel and C. Löffler, Commitment, first-mover and second-mover advantage, Journal of Economics, 94 (2008), 143-166. [4] S. Sklivas, The strategic choice of managerial incentives, Rand Journal of Economics, 18 (1987), 452-458. [5] G. Stamatopoulos, Cournot and Stakelberg equilibrium under strategic delegation: an equivalence result, Theory and Decision, 81 (2016), 553-570. doi: 10.1007/s11238-016-9548-x. [6] J. Vickers, Delegation and the theory of the firm, Economic Journal, 95 (1985), 138-147.

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##### References:
 [1] C. Fershtman and K. L. Judd, Equilibrium incentives in oligopoly, American Economic Review, 77 (1987), 927-940. [2] E. Gal-Or, First mover and second mover advantages, International Economic Review, 26 (1985), 649-653. doi: 10.2307/2526710. [3] M. Kopel and C. Löffler, Commitment, first-mover and second-mover advantage, Journal of Economics, 94 (2008), 143-166. [4] S. Sklivas, The strategic choice of managerial incentives, Rand Journal of Economics, 18 (1987), 452-458. [5] G. Stamatopoulos, Cournot and Stakelberg equilibrium under strategic delegation: an equivalence result, Theory and Decision, 81 (2016), 553-570. doi: 10.1007/s11238-016-9548-x. [6] J. Vickers, Delegation and the theory of the firm, Economic Journal, 95 (1985), 138-147.
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