American Institute of Mathematical Sciences

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April  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

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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[4]

A. Brandão, J. Pinho and H. Vasconcelos, Asymmetric collusion with growing demand,, Journal of Industry, 14 (2014), 429.   Google Scholar

[5]

D. R. Collie, Sustaining Collusion with Asymmetric Costs,, mimeo, (2004).   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[8]

J. W. Friedman, A non-cooperative equilibrium for supergames,, Review of Economic Studies, 38 (1971), 1.   Google Scholar

[9]

M. Ganslandt, L. Persson and H. Vasconcelos, Endogenous mergers and collusion in asymmetric market structures,, Economica, 79 (2012), 766.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[12]

K.-U. Kühn, The Coordinated Effects of Mergers in Differentiated Products Markets,, CEPR Discussion Paper no. 4769, (4769).   Google Scholar

[13]

M. C. Levenstein and V. Y. Suslow, What determines cartel success?,, Journal of Economic Literature, 44 (2006), 43.   Google Scholar

[14]

J. Miklós-Thal, Optimal collusion under cost asymmetry,, Economic Theory, 46 (2011), 99.  doi: 10.1007/s00199-009-0502-9.  Google Scholar

[15]

M. Motta, Competition Policy: Theory and Practice,, $7^{th}$ printing, (2004).  doi: 10.1017/CBO9780511804038.  Google Scholar

[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.  Google Scholar

[17]

M. K. Perry and R. H. Porter, Oligopoly and the incentive for horizontal merger,, American Economic Review, 75 (1985), 219.   Google Scholar

[18]

H. Vasconcelos, Tacit collusion, cost asymmetries and mergers,, RAND Journal of Economics, 36 (2005), 39.   Google Scholar

[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.  Google Scholar

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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[4]

A. Brandão, J. Pinho and H. Vasconcelos, Asymmetric collusion with growing demand,, Journal of Industry, 14 (2014), 429.   Google Scholar

[5]

D. R. Collie, Sustaining Collusion with Asymmetric Costs,, mimeo, (2004).   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[8]

J. W. Friedman, A non-cooperative equilibrium for supergames,, Review of Economic Studies, 38 (1971), 1.   Google Scholar

[9]

M. Ganslandt, L. Persson and H. Vasconcelos, Endogenous mergers and collusion in asymmetric market structures,, Economica, 79 (2012), 766.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[12]

K.-U. Kühn, The Coordinated Effects of Mergers in Differentiated Products Markets,, CEPR Discussion Paper no. 4769, (4769).   Google Scholar

[13]

M. C. Levenstein and V. Y. Suslow, What determines cartel success?,, Journal of Economic Literature, 44 (2006), 43.   Google Scholar

[14]

J. Miklós-Thal, Optimal collusion under cost asymmetry,, Economic Theory, 46 (2011), 99.  doi: 10.1007/s00199-009-0502-9.  Google Scholar

[15]

M. Motta, Competition Policy: Theory and Practice,, $7^{th}$ printing, (2004).  doi: 10.1017/CBO9780511804038.  Google Scholar

[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.  Google Scholar

[17]

M. K. Perry and R. H. Porter, Oligopoly and the incentive for horizontal merger,, American Economic Review, 75 (1985), 219.   Google Scholar

[18]

H. Vasconcelos, Tacit collusion, cost asymmetries and mergers,, RAND Journal of Economics, 36 (2005), 39.   Google Scholar

[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.  Google Scholar

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