CHAPTER 5. DYNAMIC CONTRACTING The alternative to writing the complete contingent contract is for the ven ture capitalist and the entrepreneur to write a much simpler contract, say a debt contract, and renegotiate the terms of the contract as more information becomes available Suppose that time is divided into T periods t=l, T. The initial loan and investment are made before date l and the final outcome of the project is observed at date t at each intervening date. some information about the eventual payoff arrives. Formally, we assume there is a sequence of random variables wt such that wt+a(ht) with probability p(ht) t+1 wt+b(ht) with probability 1-p(ht) where a(ht)>b(ht) and0< p(ht)< 1, h1= wl is a constant, wT=w, and the history ht=(w1,. t)is common knowledge at each date t Let dt denote the face value of the debt chosen at date t and let mt denote the cumulative transfers made to the firm up to and including date t. The rules of the game are as follows The firm and the venture capitalist are assumed to have chosen an initial contract(do, mo) before the first date At each date t, there is a pre-existing contract (d-1, mt-1). The firm proposes a new contract(dt, mt The venture capitalist accepts or rejects the proposal If the proposal is accepted, the venture capitalist makes a net transfer mt -mt_i to the firm and the firms debt is changed to d. If the proposal is rejected, nothing happens and the pre-existing contract at the next date will be(dt, mt)=(dt-1, mt-1) At the final date t=T, there is no scope for renegotiation. The firm receives the payoff maxus -dT-1, 0+mT-1 and the venture capitalist receives the payoff mindr-1, wr)-mT-1 A subgame perfect equilibrium of the game achieves the first best risk sharing allocation6 CHAPTER 5. DYNAMIC CONTRACTING The alternative to writing the complete contingent contract is for the ven￾ture capitalist and the entrepreneur to write a much simpler contract, say a debt contract, and renegotiate the terms of the contract as more information becomes available. Suppose that time is divided into T periods t = 1, ..., T. The initial loan and investment are made before date 1 and the final outcome of the project is observed at date T. At each intervening date, some information about the eventual payoff arrives. Formally, we assume there is a sequence of random variables {wt} such that wt+1 = ½ wt + a(ht) with probability p(ht) wt + b(ht) with probability 1 − p(ht) , where a(ht) > b(ht) and 0 < p(ht) < 1, h1 = w1 is a constant, wT = w, and the history ht = (w1, ..., wt) is common knowledge at each date t. Let dt denote the face value of the debt chosen at date t and let mt denote the cumulative transfers made to the firm up to and including date t. The rules of the game are as follows: • The firm and the venture capitalist are assumed to have chosen an initial contract (d0, m0) before the first date. • At each date t, there is a pre-existing contract (dt−1, mt−1). The firm proposes a new contract (dt, mt). • The venture capitalist accepts or rejects the proposal. • If the proposal is accepted, the venture capitalist makes a net transfer mt − mt−1 to the firm and the firm’s debt is changed to dt. If the proposal is rejected, nothing happens and the pre-existing contract at the next date will be (dt, mt)=(dt−1, mt−1). • At the final date t = T, there is no scope for renegotiation. The firm receives the payoff max{wT − dT−1, 0} + mT−1 and the venture capitalist receives the payoff min{dT −1, wT } − mT−1. A subgame perfect equilibrium of the game achieves the first best risk sharing allocation