Adverse Selection & Renegotiation in Procurement (The Review of Economic Studies 1990) work of: Jean-Jacques Laffont & Jean Tirole presented by: Deepak Hegde & Rob Seamans February 6, 2006

1.0 Motivation and Outline Optimal incentive scheme in a single-period trades off minimizing information rent to the high type while providing incentives to reduce costs Prior literature has dealt with multiple periods by using Long Term contract (LT) or 2 Short Term contracts (ST. Problem with LT: may not be conditionally optimal. In case first period results in high costs, it may be better for both parties to agree to higher incentives to the agent to reduce cost in period -2. Problem with ST: need to compensate good type more to reveal type, and hence danger of bad type pretending to be good type and playing a “take the money and run” strategy. Laffont & Tirole offer a tradeoff between advantages of ex ante commitment not to renegotiate contract and ex post mutually beneficial renegotiation by offering two contracts, one LT and one ST, where renegotiation occurs in second period. Setup –Agent realizes a project for principal in each period –Project’s cost (common information) depends on agent’s type and cost- reducing effort, payment to agent decreases with realized costs

2.0 The Model & Variables

2.1 The Basic Model under Incomplete Information Taking FOCs:

2.1 The Basic Model under Incomplete Information – cont’d Proposition 1. The optimal (static or dynamic) commitment solution is characterized by:

2.2 Optimal pooling allocation

3.0 Renegotiation- Proof Second Period Contracts

3.0 Renegotiation- Proof Second Period Contracts – cont’d

Taking FOCs:

3.2 Proposition 2

4.0 Characterization of Optimal Contract

4.0 Characterization of Optimal Contract – cont’d Theorem 1 “The principal offers the agent a choice between two contracts in the first period. The first is picked by the good type only and yields the efficient cost in both periods. In the second contract, both types produce at the same cost level in the first period, and the second-period allocation is the conditionally optimal one given posterior beliefs v 2 in [0,v 1 ].” Theorem 2 “The first period cost in the pooling branch c 1 (x) is independent of the discount factor (for a given x), and is an increasing function of the probability x that the good type separates in the first period. In a pooling equilibrium (x=0), c1(0) = c p (v 1 ), and in a separating equilibrium (x=1), c 1 (1) = c - (v 1 ).”

4.0 Characterization of Optimal Contract – cont’d Remarks: 1.Rent given to good type in “commitment and renegotiation” is higher than in case of commitment. 2. Principal essentially offers choice between a long term contract and a short term contract. Short term contract is followed by a conditionally optimal contract in the second period.

5.0 How much pooling?

5.0 How much pooling? (continued)

8.0 Summary

Appendix 1– Benchmark Case, Complete Information, Utilitarian Regulator Optimal regulatory allocation: Welfare:

Appendix 4.0 Characterization of Optimal Contract

Appendix 4.0 Characterization of Optimal Contract– cont’d Solution strategy: Find out what binds, break into two parts and solve.

Appendix 4.0 Characterization of Optimal Contract– cont’d 4.3 binds because last period (Lemma 2) Lemma 3: The optimal a 2 equals c - (v 2 ) Proof: By Bayes rule, v 2 <v 1. By Proposition 1, dc/dv>0, so c(v 2 )<c(v 1 ). Equation 4.5 is strictly convex in a 2, so optimal solution is c - (v 2 ).

Appendix 4.0 Characterization of Optimal Contract– cont’d Minimization of 4.2 with respect to a 1 yields: Note that we get the same pooling solution from earlier when x=0, and the result from Proposition 1 when x=1 (separating).

Appendix proof of theorem 3