14.123  Microeconomic Theory III

Re: Problem 4, I thought it may be useful to remember the following fact, which you should have learned in 14.122 or 14.12. Suppose the the continuation values after the rejection at some t is (v_1,v-2), which may depend on the realizations of the signals. Then, in any subgame-perfect equilibrium (or any sequential equilibrium) it must be that the responder j accepts an offer x if and only if E[u_j(x_j)|Info] is greater than or equal to v_j. It is also true in any equilibrium that the proposer i offers x* that maximizes E[u_i(x_i)|Info] subject to E[u_j(x_j)|Info] is greater than or equal to v_j. Of course x* is Pareto efficient.

Best

Muhamet