There are three agents. When state is B, they get signal b for sure. When G, two of the three agents get signal g and the rest get signal b (probability that an agent get g is 2/3).
(a) Derive Pr[G|b]
(b) Identify the set of p’s for which G is common p-believed.
(c) Consider a game where each agent has two actions, invest and not invest.
The cost of investment is c and a player’s investment is successful and yields a gross return of 1 if and only if the state is G and at least one more player also invests. If only one player invests and the others do not, then the gross return is 0.
Identify the set of c’s for which there is an equilibrium where everyone who knows state is G invests.
There are two agents. Agents observe signals following from the following table four times (signals are drawn independently in each trial) where ϵ is a small number.
G g b
g 3/4 − ϵ ϵ b ϵ
1/4 − ϵ
B g b
g 1/4 − ϵ ϵ b ϵ 3/4 − ϵ
(a) Find Pr[G|bbbg] and Pr[G|ggbb], where bbbg means an agent gets signal b in the first three periods and then g and ggbb is defined likewise.
(b) Identify the set C 12(G).