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.

1. Introduction.
1. The model.
2. Probability of winning and a description of equilibrium.
3. Equilibrium strategy of agents with high signals.
4. The probability of winning and strategies.
5. Solving the equilibrium equation.
6. Some numerics.
7. Independent signals.
1. Appendix: Some proofs.
2. Appendix: The nonlinear contraction operator