American Institute of Mathematical Sciences

Advanced
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), 191-225. 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), 1159-1171. 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), 92-117. 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, Competition and Trade, 14 (2014), 429-472. Google Scholar

[5]

D. R. Collie, Sustaining Collusion with Asymmetric Costs, mimeo, 2004, Cardiff University. Google Scholar

[6]

O. Compte, F. Jenny and P. Rey, Capacity constraints, mergers and collusion, European Economic Review, 46 (2002), 1-29. 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), 17-25. doi: 10.2307/134972.  Google Scholar

[8]

J. W. Friedman, A non-cooperative equilibrium for supergames, Review of Economic Studies, 38 (1971), 1-12. Google Scholar

[9]

M. Ganslandt, L. Persson and H. Vasconcelos, Endogenous mergers and collusion in asymmetric market structures, Economica, 79 (2012), 766-791. Google Scholar

[10]

J. E. Harrington, Jr., Collusion among asymmetric firms: The case of different discount factors, International Journal of Industrial Organization, 7 (1989), 289-307. 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), 767-792. doi: 10.2307/2527033.  Google Scholar

[12]

K.-U. Kühn, The Coordinated Effects of Mergers in Differentiated Products Markets, CEPR Discussion Paper no. 4769, 2004. Google Scholar

[13]

M. C. Levenstein and V. Y. Suslow, What determines cartel success?, Journal of Economic Literature, 44 (2006), 43-95. Google Scholar

[14]

J. Miklós-Thal, Optimal collusion under cost asymmetry, Economic Theory, 46 (2011), 99-125. doi: 10.1007/s00199-009-0502-9.  Google Scholar

[15]

M. Motta, Competition Policy: Theory and Practice, $7^{th}$ printing, Cambridge University Press, Cambridge, UK, 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), 59-74. 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), 219-227. Google Scholar

[18]

H. Vasconcelos, Tacit collusion, cost asymmetries and mergers, RAND Journal of Economics, 36 (2005), 39-62. Google Scholar

[19]

F. Verboven, Collusive behavior with heterogeneous firms, Journal of Economic Behavior and Organization, 33 (1997), 121-136. 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), 191-225. 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), 1159-1171. 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), 92-117. 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, Competition and Trade, 14 (2014), 429-472. Google Scholar

[5]

D. R. Collie, Sustaining Collusion with Asymmetric Costs, mimeo, 2004, Cardiff University. Google Scholar

[6]

O. Compte, F. Jenny and P. Rey, Capacity constraints, mergers and collusion, European Economic Review, 46 (2002), 1-29. 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), 17-25. doi: 10.2307/134972.  Google Scholar

[8]

J. W. Friedman, A non-cooperative equilibrium for supergames, Review of Economic Studies, 38 (1971), 1-12. Google Scholar

[9]

M. Ganslandt, L. Persson and H. Vasconcelos, Endogenous mergers and collusion in asymmetric market structures, Economica, 79 (2012), 766-791. Google Scholar

[10]

J. E. Harrington, Jr., Collusion among asymmetric firms: The case of different discount factors, International Journal of Industrial Organization, 7 (1989), 289-307. 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), 767-792. doi: 10.2307/2527033.  Google Scholar

[12]

K.-U. Kühn, The Coordinated Effects of Mergers in Differentiated Products Markets, CEPR Discussion Paper no. 4769, 2004. Google Scholar

[13]

M. C. Levenstein and V. Y. Suslow, What determines cartel success?, Journal of Economic Literature, 44 (2006), 43-95. Google Scholar

[14]

J. Miklós-Thal, Optimal collusion under cost asymmetry, Economic Theory, 46 (2011), 99-125. doi: 10.1007/s00199-009-0502-9.  Google Scholar

[15]

M. Motta, Competition Policy: Theory and Practice, $7^{th}$ printing, Cambridge University Press, Cambridge, UK, 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), 59-74. 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), 219-227. Google Scholar

[18]

H. Vasconcelos, Tacit collusion, cost asymmetries and mergers, RAND Journal of Economics, 36 (2005), 39-62. Google Scholar

[19]

F. Verboven, Collusive behavior with heterogeneous firms, Journal of Economic Behavior and Organization, 33 (1997), 121-136. doi: 10.1016/S0167-2681(97)00025-5.  Google Scholar

[1]

Jun Li, Hairong Feng, Mingchao Wang. A replenishment policy with defective products, backlog and delay of payments. Journal of Industrial & Management Optimization, 2009, 5 (4) : 867-880. doi: 10.3934/jimo.2009.5.867
[2]

Andrea Davini, Lin Wang. On the vanishing discount problem from the negative direction. Discrete & Continuous Dynamical Systems, 2021, 41 (5) : 2377-2389. doi: 10.3934/dcds.2020368
[3]

Kamil Rajdl, Petr Lansky. Fano factor estimation. Mathematical Biosciences & Engineering, 2014, 11 (1) : 105-123. doi: 10.3934/mbe.2014.11.105
[4]

Noriaki Kawaguchi. Maximal chain continuous factor. Discrete & Continuous Dynamical Systems, 2021, 41 (12) : 5915-5942. doi: 10.3934/dcds.2021101
[5]

Apostolis Pavlou. Asymmetric information in a bilateral monopoly. Journal of Dynamics & Games, 2016, 3 (2) : 169-189. doi: 10.3934/jdg.2016009
[6]

Armands Gritsans, Felix Sadyrbaev. The Nehari solutions and asymmetric minimizers. Conference Publications, 2015, 2015 (special) : 562-568. doi: 10.3934/proc.2015.0562
[7]

F. M. Bass, A. Krishnamoorthy, A. Prasad, Suresh P. Sethi. Advertising competition with market expansion for finite horizon firms. Journal of Industrial & Management Optimization, 2005, 1 (1) : 1-19. doi: 10.3934/jimo.2005.1.1
[8]

Caichun Chai, Tiaojun Xiao, Eilin Francis. Is social responsibility for firms competing on quantity evolutionary stable?. Journal of Industrial & Management Optimization, 2018, 14 (1) : 325-347. doi: 10.3934/jimo.2017049
[9]

Avner Friedman, Xiulan Lai. Antagonism and negative side-effects in combination therapy for cancer. Discrete & Continuous Dynamical Systems - B, 2019, 24 (5) : 2237-2250. doi: 10.3934/dcdsb.2019093
[10]

Claude Carlet, Sylvain Guilley. Complementary dual codes for counter-measures to side-channel attacks. Advances in Mathematics of Communications, 2016, 10 (1) : 131-150. doi: 10.3934/amc.2016.10.131
[11]

Hua Huang, Weiwei Wang, Chengwu Lu, Xiangchu Feng, Ruiqiang He. Side-information-induced reweighted sparse subspace clustering. Journal of Industrial & Management Optimization, 2021, 17 (3) : 1235-1252. doi: 10.3934/jimo.2020019
[12]

Tatsien Li, Bopeng Rao, Zhiqiang Wang. A note on the one-side exact boundary controllability for quasilinear hyperbolic systems. Communications on Pure & Applied Analysis, 2009, 8 (1) : 405-418. doi: 10.3934/cpaa.2009.8.405
[13]

Jianfeng Feng, Mariya Shcherbina, Brunello Tirozzi. Stability of the dynamics of an asymmetric neural network. Communications on Pure & Applied Analysis, 2009, 8 (2) : 655-671. doi: 10.3934/cpaa.2009.8.655
[14]

Xiong Li. The stability of the equilibrium for a perturbed asymmetric oscillator. Communications on Pure & Applied Analysis, 2006, 5 (3) : 515-528. doi: 10.3934/cpaa.2006.5.515
[15]

D. Bonheure, C. Fabry. A variational approach to resonance for asymmetric oscillators. Communications on Pure & Applied Analysis, 2007, 6 (1) : 163-181. doi: 10.3934/cpaa.2007.6.163
[16]

Lixia Wang, Shiwang Ma. Unboundedness of solutions for perturbed asymmetric oscillators. Discrete & Continuous Dynamical Systems - B, 2011, 16 (1) : 409-421. doi: 10.3934/dcdsb.2011.16.409
[17]

Xiong Li. The stability of the equilibrium for a perturbed asymmetric oscillator. Communications on Pure & Applied Analysis, 2007, 6 (1) : 69-82. doi: 10.3934/cpaa.2007.6.69
[18]

Juan Pablo Rincón-Zapatero. Hopf-Lax formula for variational problems with non-constant discount. Journal of Geometric Mechanics, 2009, 1 (3) : 357-367. doi: 10.3934/jgm.2009.1.357
[19]

Beatris Adriana Escobedo-Trujillo, Alejandro Alaffita-Hernández, Raquiel López-Martínez. Constrained stochastic differential games with additive structure: Average and discount payoffs. Journal of Dynamics & Games, 2018, 5 (2) : 109-141. doi: 10.3934/jdg.2018008
[20]

Beatris A. Escobedo-Trujillo. Discount-sensitive equilibria in zero-sum stochastic differential games. Journal of Dynamics & Games, 2016, 3 (1) : 25-50. doi: 10.3934/jdg.2016002

 Impact Factor: 

Tools

Metrics

  • PDF downloads (158)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences | Privacy Policy