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5. [20] Consider a contest where two contestants, i e (1,2), compete for a prize worth v (in utility terms). The probability of contestant i wining the compe- P(e1,e2)2 where es is the effort exerted by contestant i. The losing contestant gets tition is ei nothing, The (utility) cost of effort is c(e) = e[. Thus, contestant is payoff is given by (a) 18] Find the symmetric Nash equilibrium effort level. (b) (4] Given an interpretation of r. Give an interpretation of what happens to the equilibrium effort level as r → 0. (e) [81 Now, suppose 2 and the contestants are restricted to putting in one of two effort levels: high (G = 3) or low (ei = 1). Find all the Nash equilibria (including mixed strategy ones).
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