The profit-sharing rule that maximizes sustainability of cartel agreements

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2016, 3(2): 143-151. doi: 10.3934/jdg.2016007

The profit-sharing rule that maximizes sustainability of cartel agreements

João Correia-da-Silva ^1, and Joana Pinho ^2,

1.	Toulouse School of Economics, 21 Allée de Brienne, 31000 Toulouse, France
2.	CEF.UP, Faculdade de Economia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-464 Porto, Portugal

Received October 2015 Revised April 2016 Published April 2016

Abstract
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We study the profit-sharing rule that maximizes the sustainability of cartel agreements when firms can make side-payments. This rule is such that the critical discount factor is the same for all firms (``balanced temptation''). If a cartel applies this rule, contrarily to the typical finding in the literature, asymmetries among firms may increase the sustainability of the cartel. In an illustrating example of a Cournot duopoly with asymmetric production costs, the sustainability of collusion is maximal when firms are extremely asymmetric.

Keywords: Collusion, balanced temptation., asymmetric firms, critical discount factor, side-payments.

Mathematics Subject Classification: Primary: 91A80; Secondary: 91A2.

Citation: João Correia-da-Silva, Joana Pinho. The profit-sharing rule that maximizes sustainability of cartel agreements. Journal of Dynamics & Games, 2016, 3 (2) : 143-151. doi: 10.3934/jdg.2016007

References:

[1]	D. Abreu, Extremal equilibria of oligopolistic supergames,, Journal of Economic Theory, 39 (1986), 191. doi: 10.1016/0022-0531(86)90025-6.
[2]	H. Bae, A price-setting supergame between two heterogeneous firms,, European Economic Review, 31 (1987), 1159. doi: 10.1016/S0014-2921(87)80011-9.
[3]	I. Bos and J. E. Harrington, Jr., Endogenous cartel formation with heterogeneous firms,, RAND Journal of Economics, 41 (2010), 92. doi: 10.1111/j.1756-2171.2009.00091.x.
[4]	A. Brandão, J. Pinho and H. Vasconcelos, Asymmetric collusion with growing demand,, Journal of Industry, 14 (2014), 429.
[5]	D. R. Collie, Sustaining Collusion with Asymmetric Costs,, mimeo, (2004).
[6]	O. Compte, F. Jenny and P. Rey, Capacity constraints, mergers and collusion,, European Economic Review, 46 (2002), 1. doi: 10.1016/S0014-2921(01)00099-X.
[7]	C. d'Aspremont, A. Jacquemin, J. J. Gabszewicz and J. A. Weymark, On the stability of collusive price leadership,, Canadian Journal of Economics, 16 (1983), 17. doi: 10.2307/134972.
[8]	J. W. Friedman, A non-cooperative equilibrium for supergames,, Review of Economic Studies, 38 (1971), 1.
[9]	M. Ganslandt, L. Persson and H. Vasconcelos, Endogenous mergers and collusion in asymmetric market structures,, Economica, 79 (2012), 766.
[10]	J. E. Harrington, Jr., Collusion among asymmetric firms: The case of different discount factors,, International Journal of Industrial Organization, 7 (1989), 289. doi: 10.1016/0167-7187(89)90025-8.
[11]	J. E. Harrington, Jr., The determination of price and output quotas in a heterogeneous cartel,, International Economic Review, 32 (1991), 767. doi: 10.2307/2527033.
[12]	K.-U. Kühn, The Coordinated Effects of Mergers in Differentiated Products Markets,, CEPR Discussion Paper no. 4769, (4769).
[13]	M. C. Levenstein and V. Y. Suslow, What determines cartel success?,, Journal of Economic Literature, 44 (2006), 43.
[14]	J. Miklós-Thal, Optimal collusion under cost asymmetry,, Economic Theory, 46 (2011), 99. doi: 10.1007/s00199-009-0502-9.
[15]	M. Motta, Competition Policy: Theory and Practice,, $7^{th}$ printing, (2004). doi: 10.1017/CBO9780511804038.
[16]	M. J. Osborne and C. Pitchik, Profit-sharing in a collusive industry,, European Economic Review, 22 (1983), 59. doi: 10.1016/0014-2921(83)90089-2.
[17]	M. K. Perry and R. H. Porter, Oligopoly and the incentive for horizontal merger,, American Economic Review, 75 (1985), 219.
[18]	H. Vasconcelos, Tacit collusion, cost asymmetries and mergers,, RAND Journal of Economics, 36 (2005), 39.
[19]	F. Verboven, Collusive behavior with heterogeneous firms,, Journal of Economic Behavior and Organization, 33 (1997), 121. doi: 10.1016/S0167-2681(97)00025-5.

show all references

References:

[1]	D. Abreu, Extremal equilibria of oligopolistic supergames,, Journal of Economic Theory, 39 (1986), 191. doi: 10.1016/0022-0531(86)90025-6.
[2]	H. Bae, A price-setting supergame between two heterogeneous firms,, European Economic Review, 31 (1987), 1159. doi: 10.1016/S0014-2921(87)80011-9.
[3]	I. Bos and J. E. Harrington, Jr., Endogenous cartel formation with heterogeneous firms,, RAND Journal of Economics, 41 (2010), 92. doi: 10.1111/j.1756-2171.2009.00091.x.
[4]	A. Brandão, J. Pinho and H. Vasconcelos, Asymmetric collusion with growing demand,, Journal of Industry, 14 (2014), 429.
[5]	D. R. Collie, Sustaining Collusion with Asymmetric Costs,, mimeo, (2004).
[6]	O. Compte, F. Jenny and P. Rey, Capacity constraints, mergers and collusion,, European Economic Review, 46 (2002), 1. doi: 10.1016/S0014-2921(01)00099-X.
[7]	C. d'Aspremont, A. Jacquemin, J. J. Gabszewicz and J. A. Weymark, On the stability of collusive price leadership,, Canadian Journal of Economics, 16 (1983), 17. doi: 10.2307/134972.
[8]	J. W. Friedman, A non-cooperative equilibrium for supergames,, Review of Economic Studies, 38 (1971), 1.
[9]	M. Ganslandt, L. Persson and H. Vasconcelos, Endogenous mergers and collusion in asymmetric market structures,, Economica, 79 (2012), 766.
[10]	J. E. Harrington, Jr., Collusion among asymmetric firms: The case of different discount factors,, International Journal of Industrial Organization, 7 (1989), 289. doi: 10.1016/0167-7187(89)90025-8.
[11]	J. E. Harrington, Jr., The determination of price and output quotas in a heterogeneous cartel,, International Economic Review, 32 (1991), 767. doi: 10.2307/2527033.
[12]	K.-U. Kühn, The Coordinated Effects of Mergers in Differentiated Products Markets,, CEPR Discussion Paper no. 4769, (4769).
[13]	M. C. Levenstein and V. Y. Suslow, What determines cartel success?,, Journal of Economic Literature, 44 (2006), 43.
[14]	J. Miklós-Thal, Optimal collusion under cost asymmetry,, Economic Theory, 46 (2011), 99. doi: 10.1007/s00199-009-0502-9.
[15]	M. Motta, Competition Policy: Theory and Practice,, $7^{th}$ printing, (2004). doi: 10.1017/CBO9780511804038.
[16]	M. J. Osborne and C. Pitchik, Profit-sharing in a collusive industry,, European Economic Review, 22 (1983), 59. doi: 10.1016/0014-2921(83)90089-2.
[17]	M. K. Perry and R. H. Porter, Oligopoly and the incentive for horizontal merger,, American Economic Review, 75 (1985), 219.
[18]	H. Vasconcelos, Tacit collusion, cost asymmetries and mergers,, RAND Journal of Economics, 36 (2005), 39.
[19]	F. Verboven, Collusive behavior with heterogeneous firms,, Journal of Economic Behavior and Organization, 33 (1997), 121. doi: 10.1016/S0167-2681(97)00025-5.

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