Irrelevance of Conjectural Variation in a Mixed Duopoly: The Case of Relative Performance and Consistent Conjectures

ABSTRACT

This study explores the equilibrium outcomes in the contexts of quantity-setting and price-setting mixed duopolies with consistent conjectures of both the social welfare maximizing public firm and the relative profit maximizing private firm. Similar to the private duopoly composed of only relative profit maximizing firms, we show that in the mixed duopoly, 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

Mixed duopoly; Relative Profit Maximization; Conjectural Variation; Consistent Conjecture*JEL Classification*: L20,
L32,
D43

Mixed duopoly; Relative Profit Maximization; Conjectural Variation; Consistent Conjecture

Cite this paper

Y. Nakamura, "Irrelevance of Conjectural Variation in a Mixed Duopoly: The Case of Relative Performance and Consistent Conjectures,"*Theoretical Economics Letters*, Vol. 3 No. 5, 2013, pp. 5-11. doi: 10.4236/tel.2013.35A2002.

Y. Nakamura, "Irrelevance of Conjectural Variation in a Mixed Duopoly: The Case of Relative Performance and Consistent Conjectures,"

References

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[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, 2013a, 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, 2013b, pp. 75-83.

[8] Y. Tanaka, “Irrelevance of Conjectural Variation in Duopoly under Relative Profit Maximization and Consistent Conjectures,” 2013c (mimeo).

[9] M. E. Schaffer, “Are Profit Maximizers the Best Survivors?” Journal of Economic Behavior and Organization, Vol. 12, No. 1, 1989, pp. 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, Vol. 64, Suppl. S1, 2012, pp. 22-31. doi:10.1111/j.1467-8586.2012.00439.x

[14] Y. Nakamura and M. Saito, “Capacity Choice in a Mixed Duopoly: The Relative Performance Approach,” Theoretical Economics Letters, Vol. 3, No. 2, 2013a, pp. 124-133. doi:10.4236/tel.2013.32020

[15] Y. Nakamura and M. Saito, “Capacity Choice in a Price-Setting Mixed Duopoly: The Relative Performance Approach,” Modern Economy, Vol. 4, No. 4, 2013b, pp. 273-280. doi:10.4236/me.2013.44031

[16] N. Singh and X. Vives, “Price and Quantity Competition in a Differentiated Duopoly,” RAND Journal of Economics, Vol. 15, No. 4, 1984, pp. 546-554. doi:10.2307/2555525

[17] T. Matsumura and M. Okamura, “Competition and Privatization Policy: The Relative Performance Approach,” 2010 (mimeo).

[18] C. Fershtman and K. Judd, “Equilibrium Incentives in Oligopoly,” American Economic Review, Vol. 77, No. 5, 1987, pp. 927-940.

[19] S. D. Sklivas, “The Strategic Choice of Managerial Incentives,” RAND Journal of Economics, Vol. 18, No. 3, 1987, pp. 452-458. doi:10.2307/2555609

[20] J. Vickers, “Delegation and the Theory of the Firm,” Economic Journal, Vol. 95, No. 380, 1985, pp. 138-147. doi:10.2307/2232877

[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, 2013a, 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, 2013b, pp. 75-83.

[8] Y. Tanaka, “Irrelevance of Conjectural Variation in Duopoly under Relative Profit Maximization and Consistent Conjectures,” 2013c (mimeo).

[9] M. E. Schaffer, “Are Profit Maximizers the Best Survivors?” Journal of Economic Behavior and Organization, Vol. 12, No. 1, 1989, pp. 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, Vol. 64, Suppl. S1, 2012, pp. 22-31. doi:10.1111/j.1467-8586.2012.00439.x

[14] Y. Nakamura and M. Saito, “Capacity Choice in a Mixed Duopoly: The Relative Performance Approach,” Theoretical Economics Letters, Vol. 3, No. 2, 2013a, pp. 124-133. doi:10.4236/tel.2013.32020

[15] Y. Nakamura and M. Saito, “Capacity Choice in a Price-Setting Mixed Duopoly: The Relative Performance Approach,” Modern Economy, Vol. 4, No. 4, 2013b, pp. 273-280. doi:10.4236/me.2013.44031

[16] N. Singh and X. Vives, “Price and Quantity Competition in a Differentiated Duopoly,” RAND Journal of Economics, Vol. 15, No. 4, 1984, pp. 546-554. doi:10.2307/2555525

[17] T. Matsumura and M. Okamura, “Competition and Privatization Policy: The Relative Performance Approach,” 2010 (mimeo).

[18] C. Fershtman and K. Judd, “Equilibrium Incentives in Oligopoly,” American Economic Review, Vol. 77, No. 5, 1987, pp. 927-940.

[19] S. D. Sklivas, “The Strategic Choice of Managerial Incentives,” RAND Journal of Economics, Vol. 18, No. 3, 1987, pp. 452-458. doi:10.2307/2555609

[20] J. Vickers, “Delegation and the Theory of the Firm,” Economic Journal, Vol. 95, No. 380, 1985, pp. 138-147. doi:10.2307/2232877