VOLUME VII
Corollary. If we have a case of symmetric valuations V1 = V2, the condition (2.1) turns into: 1 + 1/p ≥ √ / √ψ, so the smaller the probability of the fair scenario, p, the more likely it is for an inner Bayesian Equilibrium to hold. The winning probabilities of both agents will depend on the
realized state of nature. We find that: Proposition 3. When p=1 or p=0, and when = ψ, the Bayesian Equilibrium found here is equal to the Nash Equilibrium found in subsection 2.1
2.3
Comparative Statics and Analysis
2.3.1
Agent with Incomplete Information
We will first take a look at the agent with incomplete information, contestant 1. The comparative statics for this agent are more intuitive and simpler than what we will see for the contestant with complete information. The extensive algebra for all the statements presented in this section can be found in the appendix of the paper. In traditional contest theory literature, as seen in Corchón (2007), agents with a higher valuation (or a lower cost) usually exert a higher level of effort. This results can be seen in our Bayesian equilibrium since (∂e1*)/(∂V1) > 0 for all values of the parameters. The effect of a variation in the opponent’s valuation, (∂e1*)/(∂V2), will only be positive if V1 > V2. This means that, while contestant 1 has a higher valuation, increases in V2