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I shall assume that the supervisor's information is "hard."By this I mean that his report is verifiable in the following sense: when he observes the state of productivity, he can convey this information to the principal in a credible way (the principal can look at the evidence and convince himself that the supervisor has announced the true state of productivity). However, the supervisor can lie and announce he has observed nothing, that is, conceal the evidence. (He can also announce the wrong state of nature, but this claim, which cannot be substantiated, is assumed to be interpreted as the absence of observation). Thus,

–  –  –

Let us briefly examine the notion ofverifiability. The report can be thought of as the communication of the outcome of a quality test on the agent's product, or as a report on other shops, divisions, or firms facing a state of productivity correlated with that of the agent, or else as a credible statement by the supervisor on the agent's activity (the supervisor makes a "convincing case"). This leads us to three questions. First, are there circumstances in which the agent cannot supply a verifiable report himself? Second, if the agent can supply a verifiable report himself, is there still room for the supervisory function? Third, are nonverifiable reports of any interest? The first two questions will be analyzed in sections 4.1 and 3.2 respectively. I will not attempt to address the third question in detail. In section 4.5 I give an example in which nonverifiable reports can be useful. In general, however, nonverifiable reports create hazards. Indeed, in the accounting literature, Ijiri, Gjesdal, and Antle (1982, 1984) have warned us against the use of"soft" (that is, nonveriThis content downloaded from 59.65.123.66 on Mon, 28 Oct 2013 01:51:38 AM All use subject to JSTOR Terms and Conditions 190 / JOURNAL OF LAW, ECONOMICS, AND ORGANIZATION 11:2, 1986 fiable) information.17In my model, in the absence of collusion, it does not matter whether information is "hard" (verifiable), as is assumed here, or "soft." If the supervisor and the agent collude, however, soft information becomes useless, as is easily seen. Thus, I focus on hard information.

If the contract is accepted, the agent learns the state of nature; and the supervisor learns his signal, that is, he observes or does not observe the state of productivity. The agent then exerts effort. The profit is realized and the supervisor produces a report (the exact timing of the report can actually be a choice variable for the principal). The principal then rewards the supervisor and the agent.

The timing is summarized in the following diagram:

- -9

–  –  –

The Symmetric Information Allocation (First Best). For purposes of comparison, I consider the case in which the state of productivity is observed by the principal. The supervisor then has no supervisory function. He receives So in all states of nature. The effort exerted by the agent is also observable by the principal. The optimal level of effort e* maximizes the profit

minus the disutility of effort:

–  –  –

At the optimum, for any state of nature, the marginal disutility of effort is equal to the marginal profit. I will denote g* g(e*) the corresponding disutility of effort. The agent also receives a wage that is independent of the state of nature: Wi = Wo + g*.

Asymmetric Information and Overt Contract. From now on, I consider the information structure described above as the four states of nature. I first derive the optimal contract, assuming that side contracts are infeasible (coalitions do not form).

Note that, when given a constant wage So, the supervisor is fully insured and obtains his reservation utility. Furthermore, he has no incentive to lie (conceal the evidence). Thus, the principal can obtain the supervisor's information at "minimal cost."

17. Antle (1984) studies soft informationand shows that even in the absence of side transfers between the auditor (supervisor)and the manager (agent), the optimal auditor'scontract may not depend on the auditor'sreport if one requires that the auditor has a dominant strategy (telling the truth in our context). Antle also allows for a supervisory effort.

–  –  –

The three-tier structure boils down to the two-tier principal/agent one, in which the principal pays a lump sum So and inherits the supervisor'sinformation structure.

Thus consider program (CF) (where CF stands for "coalition free"):

–  –  –

The agent's individual rationality constraint (AIR)states that the agent must obtain at least his reservation utility. The agent's incentive compatibility constraint (AIC) comes from the fact that the principal has incomplete information about the state of nature in state 3. The agent can always exert effort (e2 - A0) in state 3 to claim the state is actually 2 and obtain wage W2.

(A similar incentive compatibility constraint also exists in state 2 [W2 g(e2) - W3 - g(e3 + AO)];but, as is usual, this constraint is not binding at the optimum. The issue is to induce the agent to reveal that the state of productivity is good, not that it is bad.) Program (CF) leads to Proposition 1: In the absence of coalitions, the optimal contract is equivalent to the optimal contract between the principal and the agent when the principal has the supervisor's information structure. The supervisor's wage is equal to So in all states





of nature. Furthermore:

–  –  –

The proof of proposition 1, which is a straightforwardextension of familiar proofs in contract theory, is supplied in the appendix. The supervisor's honesty implies that the principalhas full informationin states of nature 1 and 4 (when the supervisor observes the true state). The first best level of effort can then be required from the agent. Optimal insurance implies that the agent's wage is the same in these two states. In states of nature 2 and 3, the principal has incomplete information about the state of productivity. The agent's wage must be higher in state 3 than in state 2, in order to provide the

–  –  –

agent with sufficient incentives not to shirk in state 3 (that is, not to claim that the productivity is low). Under asymmetric information, the principal must rewarda high performanceand punish a low one. The optimum also involves a suboptimaleffort in the low state of productivity (this makes it less attractiveto shirk in the good state of productivity, once the corresponding reduction in W2 is taken into account).

COALITION

3.2. SUPERVISOR/AGENT Let us now introduce the possibility of a coalition between the supervisor and the agent. Suppose that after (or simultaneously with) having signed the main contract offered by the principal, and before the uncertainty is resolved, the supervisor and the agent sign a side (covert) contract. This side contract specifies transfer t(x,r) from the agent to the supervisor as a function of the realized profit and the supervisor's report. (Making t depend also on the supervisor's signal would not affect the analysis, because as is easily seen, the signal can in equilibrium be recovered from the profit and the report.) The supervisor's and the agent's gross incomes become {S(x,r) + t (x,r)} and {W(x,r) - t(x,r)}. Note that I formalize the side transfert as being monetary.

I assume that either the side transfer t is not observable by the principal or the main contract does not contain a clause forbidding further bilateral contracts (the same outcome arises if the principal signs a main contract with the supervisor only, and lets the supervisor "subcontract"with an agent any way the supervisor wants).

Under a supervisor/agent coalition, the allocation given by proposition 1 is no longer sustainable. In state of nature 4, the supervisor is indifferent between reporting he has observed the good state of productivity and "remaining silent" (claiming he has observed nothing); but the agent prefers the supervisor to remain silent. Thus, the agent has an incentive to bribe the supervisor to prevent him from revealing that the technology is favorable to the agent.

More generally, the supervisor and the agent ought to sign a side contract that induces the supervisor to report r in the feasible set of reports so as to maximize the total wage bill {W(x,r) + S(x,r)}for any state of nature and profit X.18 The issue of how the supervisor and the agent split the surplus generated by their side contract is a matter of bargainingpower and is not germane to the points made here. Therefore, I will make only the following assumptions on the bargaining process.

18. Note that this point and the subsequent analysis would not be affected if the principal asked the agent to send a "message"as well. The agent and the supervisor can always coordinate on what message to send. Thus, the wage bill can only depend on :Iardinformation (verifiable report and profit).

–  –  –

Al. The supervisor and the agent choose a side contract that is Pareto optimal for these two parties.

A2. Each of the two parties can guarantee itself the no-side-contract outcome.

Given that the supervisor and the agent bargain under symmetric information, these two assumptions are indeed quite weak.

I use the following methodology: in a first step I derive a set of contraints that thefinal (post side contract)allocation must satisfy;to the usual individual rationality and individual incentive compatibility constraints, I add a set of "coalitionincentive compatibility constraints."In the second step I maximize the principal's expected payoff subject to this enlarged set of constraints, assuming that no coalition is formed. The third (and trivial) step consists in showing that the optimal contract does not generate a side contract between the supervisor and the agent (that is, is coalition-proof).

Let us startby deriving a set of constraintsthat must be satisfied by the final allocation. This allocation will be represented by {Si,Wi,ei}for all i (Si and Wi now include the side transfer).

i) The participation-or individual rationality (IR)-constraints for the supervisor and the agent must be satisfied. Otherwise, under rational expectations, the main contract would not be signed. Thus, we can impose

–  –  –

ii) The agent in state of nature 3 should not claim that the state of nature is 2 (remember he is the only party who can distinguish between those two states).

To claim so, he would have to exert effort (e2 - AO). Thus, the incentive compatibility constraint for the agent is

–  –  –

Similarly, in state of nature 2, the agent should not behave as in state of nature

3. But, as usual, this second incentive constraint will not be binding and can be ignored for the moment. We will later check to see that it indeed is satisfied.

iii) Let us now derive the coalition incentive constraints (CIC). In states of nature 1 and 4, the supervisor can conceal his information. Hence, if the supervisor and the agent choose a Pareto-optimalside contract, the total wage bill net of the disutility of effort in states 1 and 4 cannot be lower than that in states 2 and 3 respectively. Thus, we get

–  –  –

Note that, if (AIC) is binding, (CIC 3) reduces to (CIC 3') S3 B S2.

There are two constraints that we ignore for the moment: the agent IC constraint in state 2 (W2 - g(e2) ? W3 - g(e3 + AO)) and the coalition IC constraint in state 2 (S2 + W2 - g(e2) ' S3 + W3 - g(e3 + AO)). These constraints will indeed be automatically satisfied by the solution to our problem.

Next, let us compute the optimal contract for the principal when the latter anticipates that no coalition forms but must respect the previous constraints.

That is, we look for the solution to program (C):

–  –  –

Note that the coalition necessarily hurts the principal, because (C) involves more constraints than (CF). The solution to (C) is derived in the appendix and is described in the following lemma.

–  –  –



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