The profit-sharing rule that maximizes sustainability of cartel agreements

Previous Article
Conformity-based behavior and the dynamics of price competition: A new rationale for fashion shifts
JDG Home
This Issue
Next Article
Localization and prices in the quadratic Hotelling model with uncertainty

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

Abstract
Related Papers

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 and 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.
[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.
[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.
[4]	A. Brandão, J. Pinho and H. Vasconcelos, Asymmetric collusion with growing demand, Journal of Industry, Competition and Trade, 14 (2014), 429-472.
[5]	D. R. Collie, Sustaining Collusion with Asymmetric Costs, mimeo, 2004, Cardiff University.
[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.
[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.
[8]	J. W. Friedman, A non-cooperative equilibrium for supergames, Review of Economic Studies, 38 (1971), 1-12.
[9]	M. Ganslandt, L. Persson and H. Vasconcelos, Endogenous mergers and collusion in asymmetric market structures, Economica, 79 (2012), 766-791.
[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.
[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.
[12]	K.-U. Kühn, The Coordinated Effects of Mergers in Differentiated Products Markets, CEPR Discussion Paper no. 4769, 2004.
[13]	M. C. Levenstein and V. Y. Suslow, What determines cartel success?, Journal of Economic Literature, 44 (2006), 43-95.
[14]	J. Miklós-Thal, Optimal collusion under cost asymmetry, Economic Theory, 46 (2011), 99-125. doi: 10.1007/s00199-009-0502-9.
[15]	M. Motta, Competition Policy: Theory and Practice, $7^{th}$ printing, Cambridge University Press, Cambridge, UK, 2004. doi: 10.1017/CBO9780511804038.
[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.
[17]	M. K. Perry and R. H. Porter, Oligopoly and the incentive for horizontal merger, American Economic Review, 75 (1985), 219-227.
[18]	H. Vasconcelos, Tacit collusion, cost asymmetries and mergers, RAND Journal of Economics, 36 (2005), 39-62.
[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.

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.
[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.
[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.
[4]	A. Brandão, J. Pinho and H. Vasconcelos, Asymmetric collusion with growing demand, Journal of Industry, Competition and Trade, 14 (2014), 429-472.
[5]	D. R. Collie, Sustaining Collusion with Asymmetric Costs, mimeo, 2004, Cardiff University.
[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.
[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.
[8]	J. W. Friedman, A non-cooperative equilibrium for supergames, Review of Economic Studies, 38 (1971), 1-12.
[9]	M. Ganslandt, L. Persson and H. Vasconcelos, Endogenous mergers and collusion in asymmetric market structures, Economica, 79 (2012), 766-791.
[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.
[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.
[12]	K.-U. Kühn, The Coordinated Effects of Mergers in Differentiated Products Markets, CEPR Discussion Paper no. 4769, 2004.
[13]	M. C. Levenstein and V. Y. Suslow, What determines cartel success?, Journal of Economic Literature, 44 (2006), 43-95.
[14]	J. Miklós-Thal, Optimal collusion under cost asymmetry, Economic Theory, 46 (2011), 99-125. doi: 10.1007/s00199-009-0502-9.
[15]	M. Motta, Competition Policy: Theory and Practice, $7^{th}$ printing, Cambridge University Press, Cambridge, UK, 2004. doi: 10.1017/CBO9780511804038.
[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.
[17]	M. K. Perry and R. H. Porter, Oligopoly and the incentive for horizontal merger, American Economic Review, 75 (1985), 219-227.
[18]	H. Vasconcelos, Tacit collusion, cost asymmetries and mergers, RAND Journal of Economics, 36 (2005), 39-62.
[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.

[1]	Jun Li, Hairong Feng, Mingchao Wang. A replenishment policy with defective products, backlog and delay of payments. Journal of Industrial and 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 and 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 and 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 and 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 and 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 and 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 and 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 and 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 and Applied Analysis, 2009, 8 (1) : 405-418. doi: 10.3934/cpaa.2009.8.405
[13]	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
[14]	Beatris Adriana Escobedo-Trujillo, Alejandro Alaffita-Hernández, Raquiel López-Martínez. Constrained stochastic differential games with additive structure: Average and discount payoffs. Journal of Dynamics and Games, 2018, 5 (2) : 109-141. doi: 10.3934/jdg.2018008
[15]	Beatris A. Escobedo-Trujillo. Discount-sensitive equilibria in zero-sum stochastic differential games. Journal of Dynamics and Games, 2016, 3 (1) : 25-50. doi: 10.3934/jdg.2016002
[16]	Jianfeng Feng, Mariya Shcherbina, Brunello Tirozzi. Stability of the dynamics of an asymmetric neural network. Communications on Pure and Applied Analysis, 2009, 8 (2) : 655-671. doi: 10.3934/cpaa.2009.8.655
[17]	Xiong Li. The stability of the equilibrium for a perturbed asymmetric oscillator. Communications on Pure and Applied Analysis, 2006, 5 (3) : 515-528. doi: 10.3934/cpaa.2006.5.515
[18]	D. Bonheure, C. Fabry. A variational approach to resonance for asymmetric oscillators. Communications on Pure and Applied Analysis, 2007, 6 (1) : 163-181. doi: 10.3934/cpaa.2007.6.163
[19]	Lixia Wang, Shiwang Ma. Unboundedness of solutions for perturbed asymmetric oscillators. Discrete and Continuous Dynamical Systems - B, 2011, 16 (1) : 409-421. doi: 10.3934/dcdsb.2011.16.409
[20]	Xiong Li. The stability of the equilibrium for a perturbed asymmetric oscillator. Communications on Pure and Applied Analysis, 2007, 6 (1) : 69-82. doi: 10.3934/cpaa.2007.6.69

Impact Factor:

Tools

Metrics

Other articles
by authors

on AIMS
João Correia-da-Silva Joana Pinho
on Google Scholar
João Correia-da-Silva Joana Pinho

[Back to Top]