Existence of a Unique Equilibrium in Asymmetric Contests with Interdependent Preferences
By relaxing the common assumption of purely self-interested preferences in contests, we study contests in which players care not only about their own material payoffs but also about other players’ payoffs, a scenario we term “interdependent preferences.” In addition, we identify three possible types of heterogeneity among players in contests. First, players may have asymmetric preferences toward each other. Second, players may have various abilities to convert expenditures to productive efforts. Third, players may face various financial constraints. This paper presents a proof of the existence and uniqueness of a pure Nash equilibrium in asymmetric contests with interdependent preferences.
Existence of a Unique Equilibrium in Asymmetric Contests with Interdependent Preferences, International Journal of Economic Behavior and Organization. Special Issue: Recent Developments of Economic Theory and Its Applications.
Vol. 3, No. 2-1,
2015, pp. 10-14.
D. Acemoglu, and M. K. Jensen, “Aggregate comparative statics,” Games and Economic Behavior, vol.81, pp. 27–49, 2013.
K. H. Baik, “Effort levels in contests with two asymmetric players,” Southern Economic Journal, vol.61, pp.367–378, 1994.
K. H. Baik, and I. G. Kim, “Delegation in contests,” European Journal of Political Economy, vol.13, pp.281–298, 1997.
G. I. Bischi, C. Chiarella, M. Kopel, and F. Szidarovszky, Nonlinear Oligopolies: Stability and Bifurcations, Berlin: Springer-Verlag, 2010.
J. Brandts, T. Saijo, and A. Schram, “How universal is behavior? A four country comparison of spite and cooperation in voluntary contribution mechanisms,” Public Choice, vol.119, pp.381–424, 2004.
J. I. Bulow, J. D. Geanakoplos, and P. D. Klemperer, “Multimarket oligopoly: Strategic substitutes and complements,” Journal of Political Economy, vol.93, pp.488–511, 1985.
T. N. Cason, T. Saijo, and T. Yamato, “Voluntary participation and spite in public good provision experiments: An international comparison,” Experimental Economics, vol.5, pp.133–153, 2002.
J. C. Coats, and W. S. Neilson, “Beliefs about other-regarding preferences in a sequential public goods game,” Economic Inquiry , vol.43, pp.614–622, 2005.
Y-K. Che, and I. Gale, “Rent dissipation when rent seekers are budget constrained,” Public Choice, vol.92, pp.109–126, 1997.
D. J. Clark, and C. Riis, “Contest success functions: An extension,” Economic Theory, vol.11, pp.201–204, 1998.
L. C. Corchón, “Comparative statics for aggregative games: The strong concavity case,” Mathematical Social Sciences, vol.28, pp.151–165, 1994.
L. C. Corchón, “The theory of contests: A survey, ”Review of Economic Design, vol.11, pp.69–100, 2007.
R. Cornes, and R. Hartley, “Asymmetric contests with general technologies,” Economic Theory, vol.26, pp.923–946, 2005.
A. Dixit, “Strategic behavior in contests,” American Economic Review, vol.77, pp.891–898, 1987.
C. Fershtman, and K. L. Judd, “Equilibrium incentives in oligopoly,” American Economic Review, vol.77, pp.927–940, 1987.
T. Guse, and B. Hehenkamp, “The strategic advantage of interdependent preferences in rent-seeking contests,” Public Choice, vol.129, pp.323–352, 2006.
A. L. Hillman, and J. C. Riley, “Political contestable rents and transfers,” Economics and Politics, vol.1, pp.17-39, 1989.
S. Hirai, and F. Szidarovszky, “Existence and uniqueness of equilibrium in asymmetric contests with endogenous prizes,” International Game Theory Review, vol.15, 1350005 (9 pages), 2013 .
S. Késenne, The Economic Theory of Professional Team Sports: An Analytical Treatment-Second Edition, Cheltenham, UK: Edward Elgar, 2014.
K. A. Konrad, “Altruism and envy in contests: An evolutionarily stable symbiosis,” Social Choice and Welfare, vol.22, pp. 479–490, 2004.
M. Kräkel, “Delegation and strategic incentives for managers in contests,” Managerial and Decision Economics, vol.23, pp. 461–470, 2002.
M. Kräkel, and D. Sliwka, “Strategic delegation and mergers in oligopolistic contests,” Journal of Economics and Business, vol.58, pp.119–136, 2006.
T. Matsumura, and N. Matsushima, “Competitiveness and stability of collusive behavior,” Bulletin of Economic Research, vol.64, pp.s22–s31, 2012.
P. Milgrom, and J. Roberts, “Rationalizability, learning, and equilibrium in games with strategic complementarities,” Econometrica, vol.58, pp.1255–1277, 1990.
J. D. Pérez-Castrillo, and T. Verdier, “A general analysis of rent-seeking games,” Public Choice, vol.73, pp.335–350, 1992.
T. Riechmann, “An analysis of rent-seeking games with relative-payoff maximizers,” Public Choice, vol.133, pp.147–155, 2007.
S. Shaffer, “Contests with interdependent preferences,” Applied Economics Letters, vol.13, pp.877–880, 2006.
S. Skaperdas, “Contest success functions,” Economic Theory, vol.7, pp.283–290, 1996.
F. Szidarovszky, and S. Yakowitz, “A new proof of the existence and uniqueness of the Cournot equilibrium,” International Economic Review, vol.18, pp.787–789, 1977.
F. Szidarovszky, and K. Okuguchi, “On the existence and uniqueness of pure Nash equilibrium in rent-seeking games,” Games and Economic Behavior, vol.18, pp.135–140, 1997.
S. Szymanski, “The economics design of sporting contests,” Journal of Economic Literature, vol.41, pp.1137–1187, 2003.
G. Tullock, “Efficient rent-seeking,” In J. M. Buchanan, R. D. Tollison and G. Tullock (Eds.)， Toward a Theory of the Rent-Seeking Society (pp.97-112)，College Station: Texas A&M University Press, 1980.
J. Vickers, “Delegation and the theory of the firm,” Economic Journal, vol.95, pp.138–147, 1985.
X. Vives, “Nash equilibrium with strategic complementarities,” Journal of Mathematical Economics, vol.19, pp.305–321, 1990.
E, Wolfstetter, Topics in Microeconomics: Industrial Organization, Auctions, and Incentives, Cambridge: Cambridge University Press, 1999.
T. Yamazaki, “On the existence and uniqueness of pure-strategy Nash equilibrium in asymmetric rent-seeking contests,” Journal of Public Economic Theory, vol.10, pp.317–327, 2008.