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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 tition is e1+e2 where e is the effort exerted by contestant i. The losing contestant gets nothing. The (utility) cost of effort is c(e)-e. Thus, contestant is payoff is given by (a) [8] 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 r0. (c) [8] Now, suppose r = 2 and the contestants are restricted to putting in one of two effort levels: high (e 3) or low (e 1). Find all the Nash equilibria (including mixed strategy ones).

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