There are two players, a seller and a buyer, and two dates.
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Hi, I would like to have some guidance in this exercise related to game theory (dynamic game):


There are two players, a seller and a buyer, and two dates. At date 1, the seller chooses his investment level I ∈ {0, i_l, i_h} at cost I, where ih > i_l > 0. At date 2, the seller may sell one unit of a good and the seller has cost c(I) of supplying it, where c'(0) = −∞, c' < 0, c'' > 0, and c(0) is less than the buyer's valuation. There is no discounting, and the socially optimal level of investment, I* is i_h, this is 1 + c'(i_h) = 0. 


Suppose that at date 2 the buyer observes the investment I and makes a take-it-or-leave-it offer to the seller. What is this offer? what is the subgame perfect equilibrium of the game?


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