Full Information Model:

Let  us  start with  the  simplest example  in  which  the  principal  has full information about  the  agent's costs  and  actions,  and  devises  an  incentive scheme for the agent.

In order to  appreciate the problem, we take the output as  a  function of 'a', the action taken by  the agent. The principal  is interested to extract best effort fiom the agent. Let the best effort is b which can be thought of as a contrast  to a,  the alternative action. Now, the problem of optimal incentive scheme s(.) can be written as  

In the above problem, (2.1) is the participation constraints whereas (2.2) is the incentive compatibility constraint (the agent finds it optimal to choose b .  The underlying mechanism of the above problem  lies in that the principal chooses agent's action  b, albeit indirectly, while  designing the incentive  payment function. The constraint, which the  principal  faces, is  to make sure that the agent would like to take the action, which the principal wants her to  take.

To understand the solution of the above maximisation problem, we can break it into two  parts.  First, ignore the incentive compatibility constraints  and consider the objective function along with the participation constraint. Recall that we have  assume full information for the principal so that we  solve  the case  when  effort  is  being observed. This means,  we  can  drop  the  agent's compatibility constraint, since we can condition pay directly on the action and do not have  to  induce  her  to take  the right  action using pay  as  function of output. We  see  that for  any  x,  the principal wants  s(x)  to be  as  small  as possible. That  is,  the principal will  pay  the agent  only  enough to meet the participation constraint:

Then the principal's problem  is  to choose  b  to maximise  (x(b))  -  e(b) ≥ u . The first order condition is x'(b)  = c'(b) and the solution is, say, h *. Second, the principal  has  to pick  a function s(.) such that it is  in  the  agent's interest to choose  b *,  given s(.). That is,  s must be  such that s(x*) - c(b*) ≥ s(x(a))  -  c(a) for all  u  in A. There are various ways  of  devising  an  appropriate incentive scheme. We consider two in the following:

Target Output Scheme:

A target output of x *  is set and  the agent is paid her reservation price  if  she reaches the target and otherwise receives punishment.