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

The profit-sharing rule that maximizes sustainability of cartel agreements

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.
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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