## B. Tsirelson | ## Contests: a unique, mixed strategy equilibrium | ## Recent works |

Michael Landsberger, Boris Tsirelson,

"Contests: a unique, mixed strategy equilibrium."

SSRN 288810.

Available online (free of charge) from Social Science Research Network:

http://papers.ssrn.com/abstract=288810

or from my site:
Postscript file, or
PDF file, or
another PDF file.

A research preprint, 31 pages, bibl. 13 refs.

Actions in games that address economic environments such as auctions
and oligopoly games are typically costly, and signals, or types, are
interdependent. Consequently, such games may not have equilibria
supported by monotone strategies, *monotone equilibria,* see
Landsberger and Tsirelson (1999, 2000). Derivation of pure strategy
non-monotone equilibria when types are interdependent and continuously
distributed has not been explored in the literature, and it is
certainly a non trivial matter; mixed-strategy equilibria pose
additional problems. We address these issues by considering a contest
game that can be interpreted as competition for research funds or
jobs.

Assuming a multinormal distribution of signals, we were able to
establish a mixed strategy equilibrium and prove that this is the
*only* equilibrium in the class of all equilibria. Various
properties of this equilibrium were established. We showed some
pitfalls one may encounter by trying to impose a-priori (reasonable)
restrictions on strategies, or trying to conduct the analysis assuming
a general class of signal distribution.

- Introduction.
- The model.
- Probability of winning and a description of equilibrium.
- Equilibrium strategy of agents with high signals.
- The probability of winning and strategies.
- Solving the equilibrium equation.
- Some numerics.
- Independent signals.
- Appendix: Some proofs.
- Appendix: The nonlinear contraction operator

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