Repeated asymmetric contest games are examined under conditions which guarantee the existence and uniqueness of pure Nash equilibrium (Hirai and Szidarovszky 2013). Conditions are derived for the local asymptotical stability of the equilibrium under continuous and discrete dynamics with gradient adjustments. In both cases, a crucial assumption is the nonexistence of a dominant player at the equilibrium level. In the case of continuous time scales, this is sufficient for stability, and in the discrete case, the speeds of adjustments have to be sufficiently small. As special cases, symmetric and semi-symmetric games are analyzed.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Baik KH (1994) Effort levels in contests with two asymmetric players. South Econ J 61:367–378
Baye M, Hoppe-Wewetzer H (2003) The strategic equivalence of rent-seeking, innovation, and patent-race games. Games Econ Behav 44:217–226
Bischi G-I, Chiarella C, Kopel M, Szidarovszky F (2010) Nonlinear oligopolies, stability and bifurcations. Springer, Berlin
Che YK, Gale I (1997) Rent dissipation when rent seekers are budget constrained. Public Choice 92:109–126
Chung TY (1996) Rent-seeking contest when the prize increases with aggregate efforts. Public Choice 87:55–66
Clark DJ, Riis C (1998) Contest success functions: a survey. Econ Theor 11:201–204
Corchón LC (2007) The theory of contests: a survey. Rev Econ Des 11:69–100
Cornes R, Hartley R (2005) Asymmetric contests with general technologies. Econ Theor 26:923–946
Hanssens DM, Parsons LJ, Schultz RL (1990) Market response models: economometric and time series analysis. Kluwer, Dordrecht
Hillman AL, Riley JC (1989) Political contestable rents and transfers. Econ Polit 1:17–39
Hirai S (2012) Existence and uniqueness of pure Nash equilibrium in asymmetric contests with endogenous prizes. Econ Bull 32:2744–2751
Hirai S, Szidarovszky F (2013) Existence and uniqueness of equilibrium in asymmetric contests with endogenous prizes. Int Game Theory Rev. https://doi.org/10.1142/S0219198913500059
Leidy MP (1994) Rent dissipation through self-regulation: the social cost of monopoly under threat of reform. Public Choice 80:105–128
Matsumoto A, Szidarovszky F (2018) Dynamic oligopolies with time delays. Springer, Singapore
Okuguchi K (2005) Existence of Nash equilibrium in endogenous rent-seeking games. In: Nowak AS, Krzysztof S (eds) Advances in dynamic games, applications in economics, finance, optimization and stochastic control. Birkhäuser, Boston, pp 445–453
Okuguchi K, Szidarovszky F (1999) The theory of oligopoly with multi-product firms, 2nd edn. Springer, Berlin
Okuguchi K, Yamazaki T (2008) Global stability of unique Nash equilibrium in Cournot oligopoly and rent-seeking game. J Econ Dyn Control 32:1204–1211
Pérez-Castrillo JD, Verdier T (1992) A general analysis of rent-seeking games. Public Choice 73:335–350
Schmidt F (2008) The stability of dynamic contests with asymmetric and endogenous prizes. Econ Bull 3:1–9
Shaffer S (2006) War, labor tournaments and contest payoffs. Econ Lett 92:250–255
Skaperdas S (1996) Contest success functions. Econ Theor 7:283–290
Szidarovszky F, Okuguchi K (1997) On the existence and uniqueness of pure Nash equilibrium in rent-seeking games. Games Econ Behav 18:135–140
Tullock G (1980) Efficient rent-seeking games. In: Buchanan M, Tollison RD, Tullock G (eds), Toward a theory of the rent-seeking society, Texas A&M, College Station, pp 97-112
Xu L, Szidarovszky F (1999) The stability of dynamic rent-seeking games. Int Game Theory Rev 1:87–102
Yamazaki T (2008) On the existence and uniqueness of pure-strategy Nash equilibrium in asymmetric rent-seeking contests. J Public Econ Theory 10:317–327
Conflicts of interest
The authors declare that there is no conflict of interest
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The authors appreciate all the suggestions made by anonymous referees, which have been helped to improve the paper. They would like to thank participants at a seminar organized by the Institute of Economic Research of Chuo University. The first author highly acknowledges the financial supports from the Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research (C) 20K01566) and Chuo University (Grant for Special Research). The usual disclaimers apply.
About this article
Cite this article
Matsumoto, A., Szidarovszky, F. Stability of dynamic asymmetric contests with endogenous prizes. J Econ Interact Coord (2020). https://doi.org/10.1007/s11403-020-00290-6
- Asymmetric contests
- Dynamic models
- Discrete dynamics
- Continuous dynamics
- Stability analysis