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Problem 5. Consider the following three prayer team production problem. Each player chooses independently and simultaneously whether to make effort. In other words, Si = {E, N } fori = 1, 2, 3. Making effort imposes a cost of 3 on the player who chooses effort (E). Each player receives the same benefit regardless of whether she made effort. The benefit amount depends on which players made effort. Suppose A is the set of players who made effort. 0 if A = 0 (nobody makes effort) 2 if A = {1} or A = {2} or A = {3} Benefit = if A = {1, 2 } 5 if A = {1,3} (4) 6 if A = {2,3} 8 if A = {1, 2,3} For example if ($1, $2, $3) = (E, E, N), then A = {1, 2} and u1 (E, E, N) = 4 - 3 = 1, u2 (E, E, N) = 4 -3 = 1 and u3( E, E, N) = 4-0 =4. (a) (10 points) Is (s), $2, $3) = (E, E, E) Nash equilibrium? Explain your answer. (b) (10 points) Find all Nash equilibria in pure strategies. Explain your answer. (Hint: Consider all possibilities of set A.)