Irrelevance of Conjectural Variation in a Private Duopoly with Consistent Conjectures: The Relative Performance Approach and Network Effects

Yasuhiko Nakamura

College of Economics, Nihon University, Tokyo, Japan.

DOI: 10.4236/me.2013.49A002                

Abstract

This paper explores the equilibrium market outcomes in the contexts of both quantity-setting and price-setting private duopolies with the consistent conjectures of two private firms, wherein they maximize the weighted sum of their own profits and their respective opponent firm’s profit. Similar to the private duopoly without network effects wherein the two private firms maximize their genuine relative profits, in the private duopoly with network effects such that both firms maximize the weighted sum of their own profits and their respective opponent firm’s profit, we show that the equilibrium outcomes in the quantity-setting competition with the consistent conjectures of both firms are equivalent to those in the price-setting competition with the consistent conjectures of both firms.

Keywords

Relative Profit Maximization; Conjectural Variation; Consistent Conjecture; Network Effects

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	T. Bresnahan, “Duopoly Models with Consistent Conjectures,” American Economic Review, Vol. 71, No. 5, 1981, pp. 934-945.
[2]	M. Perry, “Oligopoly and Consistent Conjectural Variations,” Bell Journal of Economics, Vol. 13, No. 1, 1982, pp. 197-205. doi:10.2307/3003440
[3]	M. Boyer and M. Moreaux, “Consistent versus Non-Consistent Conjectures in Duopoly Theory: Some Examples,” Journal of Industrial Economics, Vol. 32, No. 1, 1983, pp. 97-110. doi:10.2307/2097988
[4]	Y. Tanaka, “Consistent Conjectures in Free Entry Oligopoly,” Economics Letters, Vol. 17, No. 1-2, 1985, pp. 15-18. doi:10.1016/0165-1765(85)90118-1
[5]	Y. Tanaka, “On Multiplicity of Consistent Conjectures in Free Entry Oligopoly,” Economics Letters, Vol. 28, No. 2, 1985, pp. 109-115. doi:10.1016/0165-1765(88)90099-7
[6]	Y. Tanaka, “Equivalance of Cournot and Bertrand Equilibria in Differentiated Duopoly under Relative Profit Maximization with Linear Demand,” Economics Bulletin, Vol. 33, No. 2, 2013, pp. 1479-1486.
[7]	Y. Tanaka, “Irrelevance of the Choice of Strategic Variables in Duopoly under Relative Profit Maximization,” Economics and Business Letters, Vol. 2, No. 2, 2013, pp. 75-83.
[8]	T. Matsumura, N. Matsushima and S. Cato, “Competitiveness and R&D Competition Revisited,” Economic Modelling, Vol. 31, 2013, pp. 541-547. doi:10.1016/j.econmod.2012.12.016
[9]	M. E. Schaffer, “Are Profit Maximizers the Best Survivors?” Journal of Economic Behavior and Organization, 12, 1, 1989, 29-45. doi:10.1016/0167-2681(89)90075-9
[10]	F. Vega-Redondo, “The Evolution of Walrasian Behavior,” Econometrica, Vol. 65, No. 2, 1997, pp. 375-384. doi:10.2307/2171898
[11]	C. Lundgren, “Using Relative Profit Incentives to Prevent Collusion,” Review of Industrial Organization, Vol. 11, No. 4, 1996, pp. 533-550. doi:10.1007/BF00157777
[12]	L. Kockesen, E. A. Ok and R. Sethi, “The Strategic Advantage of Negatively Interdependent Preferences,” Journal of Economic Theory, Vol. 92, No. 2, 2000, pp. 274-299. doi:10.1006/jeth.1999.2587
[13]	T. Matsumura and N. Matsushima, “Competitiveness and Stability of Collusive Behavior,” Bulletin of Economic Research 64, Supplement, Vol. 64, Suppl. 1, 2012, pp. 22-31. doi:10.1111/j.1467-8586.2012.00439.x
[14]	M. Katz and C. Shapiro, “Network Externalities, Competition, and Compatibility,” American Economic Review, Vol. 75, No. 3, 1985, pp. 424-440.
[15]	S. Hoernig, “Strategic Delegation under Price Competition and Network Effects,” Economics Letters, Vol. 117, No. 2, 2012, 487-489. doi:10.1016/j.econlet.2012.06.045
[16]	Y. Nakmaura, “Social Welfare under Quantity Competition and Price Competition in a Mixed Duopoly with Network Effects: An Analysis,” Theoretical Economics Letters, Vol. 3, No. 4, 2013, pp. 211-215. doi:10.4236/tel.[phone]
[17]	Y. Nakmaura, “Endogenous Timing in Price-Setting Private and Mixed Duopoly with Network Effects,” 2013, Mimeo.
[18]	Y. Nakamura and M. Saito, “Capacity Choice in a Mixed Duopoly: The Relative Performance Approach,” Theoretical Economics Letters, Vol. 3, No. 2, 2013, pp. 124-133. doi:10.4236/tel.[phone]
[19]	Y. Nakamura and M. Saito, “Capacity Choice in a Price-Setting Mixed Duopoly: The Relative Performance Approach,” Modern Economy, Vol. 4, No. 4, 2013, pp. 273-280. doi:10.4236/me.2013.44031
[20]	Y. Nakamura, “Price versus Quantity in a Mixed Duopoly: The Case of Relative Profit Maximization,” 2013, Mimeo.
[21]	F. Y. Edgeworth, “Mathematical Physics,” P. Kegan, London, 1881.
[22]	R. M. Cyert and M. H. de Groot, “An Analysis of Cooperation and Learning in a Duopoly Context,” American Economic Review, Vol. 63, No. 1, 1973, pp. 24-37.
[23]	Y. Tanaka, “Irrelevance of Conjectural Variation in Duopoly under Relative Profit Maximization and Consistent Conjectures,” 2013, Mimeo.