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Employees then have lower incentives to develop knowledge specific to their positions or to their productive teamwork with other employees. Also, the moral hazard issue within teams of employees becomes more severe in the absence of a repeated relationship. Furthermore, an organization ought to encourage certain types of side transferssuch as mutual help. Of course, such informal (covert) transfers can be used as vehicles for the formation of coalitions ("if you release this information about me, I will not help you adapt to your next task or problem"). But it is widely recognized by sociologists that without the countless acts of cooperation that take place everyday between members, most organizationswould break down. They would also be poorly equipped to adapt to changes (which require an unusual amount of cooperation). In a similar vein, the benefits from authority are eliminated by the introduction of rules; as is now well recognized, many contingencies affecting an organization are hard to foresee or are costly to describe in advance.

Allowing one of its members to make decisions when contingencies not gives flexibility to the organizacontracted for (giving him or her "authority") tion (for instance, relative to rigid ex ante decisions). Of course, the member who is given authority acquires power because his or her decisions affect the other members, and this power can be used to generate favors. Again, the advantages and drawbacks of the authority relationship must be weighted against those of alternative arrangements(see also the discussion on discretion in multiagent situations).

The moral of this very incomplete discussion of the limits to the control of side transfers is that the very factors that give rise to coalitions may also give rise to desirable effects. This means that side transferswill be curbed (when possible) only if these other effects are small. A careful analysis of the tradeoffs involved here would be quite worthwhile.

## APPENDIX

If -ywere equal to 0, the incentive constraint would be nonbinding and the first best solution would obtain. But we know that this first best solution is not incentive-compatible for the agent. Hence, y is strictly positive, which, together with (5) and the strict convexity of g, implies that e2 e*.

The ranking of the agent's utility levels in the various states of nature is given by equations (1) through (4).

The second order conditions are easily checked.

A.2. PROOFOF LEMMA1 (SUPERVISOR/AGENT COALITION) Let us know introduce the supervisor'sIR constraint and the coalition incentive constraints. We ignore (CIC 1); we will later check that this constraint is satisfied. The new Lagrangianis

First, notice that for i # 2, Lc depends on ei and Wi only through (ei - Wi) and (Wi - g(ei)). The optimum maximizes (ei - g(ei)), which leads to

Let us show that the agent IC constraint is binding, i.e.,that qy 0.

Suppose that y = 0. Equations (7), (8), (11), and (12) imply that Borch's

**rule hold between states 2 and 3:**

Let us now show that (CIC 3) is binding, i.e., that II 0. Suppose that II = 0. Equations (7) and (8) imply that S3 S2, which is impossible from (CIC 3) and the fact that (AIC) is binding. So, I 0, which implies that S2 = S3 From (6) and (7), S1 S2, and from (6) and (8) and the fact that S2 = S3 S1, E H; (6) and (9) imply that S1 S4.

Next, let us consider the agent's wage. Equations (10), (11), and (13) imply that W4 - g* W1 - g* W2 - g(e2). Also, from (CIC 2), W3 + S3 = W4 + S4, which implies that W3 W4.

Last, observe that from (14), g' (e2) 1 or, e2 e*.

Checking that (CIC 1) is satisfied is trivial, as S1 S2 and W1 - g* W2- g(e2).

## A.3. PROOFS OF PROPOSITIONS 3 AND 4 (SUPERVISOR'S RISK NEUTRALITY

## AND EXTREME RISK AVERSION)

Proposition 3. We know that for any specification of preferences, the principal cannot do better than in the collusion-free case, because he is facing more constraints. Conversely, let us show that he can do as well as in the collusion-free case if the supervisor is risk-neutral. Suppose he sells the vertical structure to the supervisor. In other words, the principal's profit is independent of the state of nature (which will imply that the final allocationsis immune to a supervisor-agent coalition). The supervisor signs the optimal contract with the agent given the supervisor's information. Thus, the agent's allocation is the same as in the collusion-free outcome. The principal can then sell the vertical structure to the supervisor at a price such that the latter's expected profit net of the sale price is equal to his reservation wage (the supervisor bears risk, but cares only about his expected wage if he is riskneutral).A more formal way of proving proposition 3 is to compare (1) through (5) to (10) through (14). These equations give the same answer (for a given,u) if one takes n = -y = 0 (i.e., if the coalition incentive constraints are not binding!); (6) through (9) are then satisfied by the appropriate choice of v.

Proposition 4. Let us now assume that the supervisor is infinitely riskaverse. Then the ratio of the supervisor's marginal utilities in two states of nature is infinite (or zero) unless the wages in these two states are equal. If the supervisor's wage is not a constant, then from (6) through (9) H = + ooor E = + oo(I am a bit informalhere; the correct way to prove proposition 4 is to take the limit when V converges to the min function). Equations (10) through (13) then show that the agent's wage is + ooor - ooin some state of nature. We assumed that it cannot fall below w. But if the agent's wage is + 00 in some state of nature, it must be - ooin another state, in order for the principalnot to lose money. Again, this is impossible.

Hence, Si is a constant (So). (CIC 2) implies that W3 = W4; that is, the principaldoes not try to distinguish between states 3 and 4. It is then clear that

the principal-agentcontractis the optimal contractgiven that the principalhas information structure {sl = _Q,S2 = s3 = S4 = 0}.

A.4. PROOFOF PROPOSITION The solution {Si, Wi, ei} to (C) satisfies conditions (a)through (e) of lemma 1. If it is coalition-proof(which we want to show), it describes what happens on the equilibrium path for each state of nature. Of course, we are free to specify what happens off the equilibrium path, as long as we do not create scope for coalitions.

Thus, let us give a more complete description of the coalition-proofmechanism that implements the solution to (C). First, the supervisor produces his report after the profit is observed. Second, the supervisor gets wage S1and S4 when he provides evidence that the state is 1 and 4, respectively (regardlessof the profit level). Third, the three parties are heavily fined whenever the {report, profit} pair is not one of the four equilibrium pairs described by the solution to (C), with the exception of the supervisor when he produces evidence about states 1 and 4 (only the other two parties are then fined if the profit differs from [0 + e*]). These three points complete the description of the mechanism.

For simplicity, I assume that side contracts between two parties are not observed by the third party. By definition of(C), the mechanism is immune to a supervisor-agent coalition.

Let us show that it is immune to a principal-agentcoalition. For this notice that in states 1 and 4, the supervisor has a dominant strategy: tell the truth.

The supervisor'swage is lowest, and it is the same in states of nature 2 and 3.

Hence, there is nothing that the principal and the agent can do to reduce the supervisor's wage.

Finally, let us show that the mechanism is immune to a principal-supervisor coalition. The object of this coalition can only be to induce the supervisor to hide the evidence in states 1 and 4. The agent's utility is higher in state 1 than in state 2. In state 1, the agent, by exerting efforte*, forces the supervisor to reveal the evidence.45 The agent's wage in state 4 is lower than in state 3 and his effort is the same in both states. Thus, a principal-supervisorcoalition cannot gain by inducing the supervisor not to reveal the evidence in state 4.

Hence, the principal-supervisor coalition cannot form either.

45. Unless the supervisor and the principal have signed a side contract that penalizes the supervisor when {x = 0 + e*, r = 8} even more than the main contract does when {x = 0 + e*, r = 0}. But the supervisor would not accept such a side contract, which would give him a very negative utility with probability pi (remember that side contracts are assumed not to be observable).

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