Consider a team with n individuals, n > 2. Each individual must choose whether to put in effort (e) or shirk (s), i. e. must choose from se, s). The team succeeds if and only if all n individuals put in effort. The cost of effort for each individual, c, is random, and is drawn uniformly from the interval [0, 1]. That is, each c is independently drawn, and uniformly distributed on [0, 1]. An individual observes his own cost realization, but not the cost realizations of anyone else in the team. Shirking has zero cost. Each individual gets a benefit of v > 1 if the team succeeds, and zero if it fails. T equals the benefit from the success or failure of the team, minus the cost of effort (if she puts in effort). An equilibrium is symmetric if every player chooses the same strategy he overall payoff to an individual a) Solve for a symmetric Bayes Nash equilibrium of this game where each player chooses e if and only if his cost is below some threshold c*, where 0 b) Are there any other symmetric Bayes Nash equilibria?
c) Does the game have an asymmetric Bayes Nash equilibrium, here some players choose s irrespective of their cost, while others choose e irrespective of their cost?