Stability of dynamic asymmetric contests with endogenous prizes

Abstract

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.

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Correspondence to Akio Matsumoto.

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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.

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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

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Keywords

  • Asymmetric contests
  • Dynamic models
  • Discrete dynamics
  • Continuous dynamics
  • Stability analysis