### 1. Technology, Preferences, and Information

Consider a consumer or a firm (the principal) who wants to delegate to an agent the production of *q* units of a good. The value for the principal of these *q *units is *S*(*q)* where *S’* *> *0, *S”* *< *0 and *S(*0) = 0. The marginal value of the good is thus positive and strictly decreasing with the number of units bought by the principal.

The production cost of the agent is unobservable to the principal, but it is common knowledge that the fixed cost is *F *and that the marginal cost θ belongs to the set . The agent can be either efficient (θ) or inefficient with respective probabilities v and 1 − v. In other words, he has the cost function

* *with probability v (2.1)

or

* *with probability 1 − v. (2.2)

We denote by the spread of uncertainty on the agent’s marginal cost. When taking his production decision the agent is informed about his type θ. We stress that this information structure is exogenously given to the players.

### 2. Contracting Variables** **

The economic variables of the problem we consider thereafter are the quantity produced *q *and the transfer *t *received by the agent. Let be the set of feasible allocations. Formally, we have

These variables are both *observable and verifiable *by a third party such as a benev- olent court of law. They can thus be included in a contract which can be enforced with appropriate out-of-equilibrium penalties if either the principal or the agent deviates from the requested output and transfer.

### 3. Timing

For most of the book, unless explicitly stated, we will maintain the timing defined in figure 2.1, where *A *denotes the agent and *P *the principal.

Figure 2.1: Timing of Contracting Under Adverse Selection

Note that contracts are offered at the *interim stage*; there is already asymmetric information between the contracting parties when the principal makes his offer.

Source: Laffont Jean-Jacques, Martimort David (2002), *The Theory of Incentives: The Principal-Agent Model*, Princeton University Press.