Consider a 2 player contributions game with private infor- mation. Each player o

Question

Consider a 2 player contributions game with private infor-

mation. Each player obtains 1 jolly if either (or both) of the players

contributes to the good. Each player incurs cost ci of contributing,

where ci = 1 with probability p, and ci = 2 with probability 1 p. As- 33

sume c1 is independent of c2. At the start of the game, Nature draws the costs for each player, and shows ci to player i but not to player j. Then the players simultaneously contribute.

(a) What is the type space for each player?

(b) What is the set of pure strategies for each player?

(c) Is there ever (for any values of p) a Bayes Nash equilibrium in

which each player contributes if and only if her cost is 1/3 ?

(d) Is there ever (for any values of p) a Bayes Nash equilibrium in which each player contributes if and only if her cost is 2/3

(e) Is there ever (for any values of p) a Bayes Nash equilibrium in which each player contributes with certainty, regardless of her cost?

Explanation / Answer

b.There are 2 pure strategies.I player 1 plays and player 2 doesnot and vice versa.

c.If each player contributes cost 1/3 only player 1 will survive.

d.If each player contributes cost 2/3 only player 2 will survive.

e.No., there is no nash equilibrium in which each player contributes regardless of her cost

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