契约理论10－合谋.pdf

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Lecture on Contract Theory 3. Complete Contracts II: Static Multilateral Contracting Collusion Background Collusion Collusion is a prevalent phenomenon in organizations, as well even in classes and families. Collusion can be cataloged to two kinds: collusion in market and collusion within organization. The former belongs to Industrial Organization Theory, so we will focus on the latter. For instance, the collusion between the union and management in labor economics, the board of directors and management in financial economics, officials and constituency in public economics, government agencies and industry or interest group in regulatory economics, and agents in contract theory (., auctions and moral hazard in teams, relative performance evaluation). As Laffont said, collusion is the most important characteristic of organization. According to Stigler (1971), three factors that determinate the formation of collusion are: mobilization costs (which depends on the nature of the interest group), transfer costs (which depends on the forms of reciprocity and supervision technology), information structure. A typical process of vertical collusion is the following figure (Tirole, 1992): Principal Grand Supervisor contract Side contractAgent Two approaches: enforceability versus self-enforceability The technology for side transfers differs in specific situations. Sometimes, the cost s of side transfer for the donor is smaller than the value s for the recipient, s, we call that is collusion; if ss, we call it cooperation (positive externality). However, more elusive is the issue of how side contracts are enforced. According to the enforceability of side contract, Tirole (1992) divides all the existing literatures into two parts: enforceable-side-contracts approach and self-enforceable-side-contracts. 1 Lecture on Contract Theory Next, we summarize the comparison as follows: EnforceabilityEmphases Enforcements Techniques Enforceability exogenous The proof of NO Classicapproach collusion contract theorySelf-enforceability endogenous The foundation Word of honor, Dynamic approach of side contractsrevenge, and mechanism reputation design Basic insights Theme 1 (collusion proofness): Under some conditions, there is no loss in designing organizations while do not leave scope for collusion. Here, side transfers do not occur. But it only predicts the final outcome but rather that the contracting structure (collusion-free grand contract or delegation) that lead to this outcome. In fact, if S is risk-neutral and has symmetrical information with A, letting S the residual claimant will not lead to (extra) cost of collusion-proof (for moral hazard problem) (Tirole, 1986). Theme 2 (equilibrium collusion): in other circumstances, letting members of the organization collude is optimal. Side transfers may be good for the organization if they are acts of cooperation (relatedly, direct transfers among members may be less costly than transfers channeled through a center). Also, collusion proof may be not good for the organization, but it too costly to fight. Theme 3 (lack of discretion and bureaucratic behavior): The fear of collusion leads organizations to reduce stakes and to make less use of decentralized information. Reducing the sensitivity of decisions to decentralized information, lowers the gains from collusion. Theme 4 (linkage of incentives): Standard sufficient statistics principles for rewarding agents do not hold in the presence of collusion. If g(y,a)h(y,a)P(T(y),a), we say T(y) is sufficient statistics of y respect to a. iiiBecause agents are linked through potential side contracting, sufficient statistics results must be extended to the level of the group. The point is that individual rewards that are less sensitive to individual performance and depend on team performance make it less likely that the supervisor will collude with particular team members to manipulate reports about individual performances. For example, the “linking punishment” in ancient China. A Model Information Following Laffont-Tirole (1991), suppose that there are three parties: a principal (P), a supervisor (S) and an agent (A). Production x is 0 or 1 (whenx1, the gross surplus to P is V). The marginal cost  is private information for A, and takes value  with probability  and  with 1. 2 Lecture on Contract Theory Utility P and A are both risk neutral. A’s utility is Uwx and his reservation utility is 0. In the absence of supervisor, P’s welfare is WVxwU. There are two alternative justifications Afor this assumption: W is a social welfare function; or A is risk averse, and shares some risk with P. No supervisor Without a supervisor, the model is a model of classical monopoly pricing or pure adverse selection. The principal’s question is to design optimal wage. P will set w if V(V) Aor V (10-1) VAand w if V (10-2) VAPoof: Consider first P give all kinds of A payment  which must satisfy A’s IR constraint. And P’s revenue is W(VU)(1)(VU)AA VAGiving , only low-cost type A will participate the game, so P’s revenue is W(VU)(V) . AThink  Why P can’t choose the quantity as control variable? Supervisor In order to discuss price discrimination or collusion, we will assume that (10-1) holds. We introduce a supervisor (S), he learns a signal {,}. If , S learns it with probability  and nothing with 1. If , S learns nothing (while his signal is useless). We assume that the signal is hard information and there is symmetric information between S and A. S’s 3 Lecture on Contract Theory report r{,}. S’s utility is S(s)s, and his reservation utility is 0 (his cost is 0, see Tirole 1986). P’s welfare is WVxwsU. ASTiming (1) A privately learns , and S generates , which means agent has interim participation constraints; (2) P offers S and A a grand contract {w,s,x}; (3) S makes a take-it-or-leave-it side contract to A (if any); (4) contracts are implemented. No collusion S is given a flat income s0 and reports truthfully. If r, then w and A has 0 rent. If r, P’s posterior belief about  is (1)ˆProb(|) (1)(1)1So, together with (10-1), we know that it is optimal to offer w. Welfare is therefore, dW(V)(1)(V)(1)(V) (10-3) Awhere, “d” stands for “price discrimination”. Under no discrimination or uniform pricing, u WV (10-4) AduClearly, WW, which means that it is benefic for P to introduce a supervisor. Collusion and policies We now allow S and A to collude, and transaction efficiency is k[0,1]. That is, if A transfers t, S receives kt. When k0, it is no-collusion case. When do S and A collude? If , collusion does not occur. Only if , S and A have incentive to collude for the information rent . In order to induce S to reveal true information when , P must pay S sk only when S reports . P’s welfare: dW[V(1)k](1)[V](1)(V)A (10-5) d(1)kSNote that: (1) A can get positive information rent when he is  but S reports , so it is ddnot a truth-telling mechanism; (2) W decreases with k and smaller than W (it means that 4 Lecture on Contract Theory collusion breaks loss to P). We call the policy the incentive policy. Theoretically P can sell the dorganization to risk-neutral S at a price equals to Ws, and S gets 0 rent. 0In contrast, P can decide not to use S’s information, then offers s0 and w (according to 10-1). This yields welfare: uuWVW (10-6) AThis latter policy can be interpreted as eliminating S’s discretion, which is called the bureaucratic policy. Note that: dduu(1)k0, WWWW; du(2), k1, WW; AS*du(3), k(0,k), WW. ASThese results correspond to Theme 1, 3 and 4. Remark 1 The difficulty of discrimination illustrates the presence of collusion. The threat of collusion induces the widespread mechanism of low-powered scheme (cost-plus contracts in procurement or cost-of-service pricing in regulation, flat wages for employees). There is a Chinese saying, “不尚贤，使民不争”. Remark 2 An alternative incentive for S to tell truth is the threat of being punished (equals to decreased wage) if caught colluding with A. for example, Kofman-Lawarree (1993). Collusion proofness Furthermore, with participation constraints ex ante, we give a collusion-proof contract (truth-telling mechanism), which maximizes expected social welfare subject to agents’ IR, IC and coalition IC (CIC). Index the three states of nature in the following way: 1: ; 2:  and ; 3:  and . A’s and S’s expected utilities are w and s. So, the iiprogram is (as 10-5): MaxVwsUS)1)(VwsUS)11AS22AS{s,w,x}ii (1)(VwsU). (AIR) w0 i(SIR) s0 i(AIC) wwˆx 233 Lecture on Contract Theory (CIC) ssk(ww) 1221The last constraint CIC means that because S and A can agree in state 1 to announce the messages they would announce in state 2, they need a punishment mechanism to avoid deviation. Intuitively, S can get more in state 1 by telling truth than when he lies and gets a bribe duk(ww). The upper bound of P’s revenue is max{W,W}. The result is related to Theme 1 21and can be referenced to Tirole (1986). Asymmetric information Suppose that S has two signals,  and , where . Consider the following mechanism: S has three potential reports r{,,}. r is a report of soft (unverifiable) ˆinformation. S first reports r and then A announces . Rewards are as follows: S receives ˆs0 unless he reports r. If r, sk if  (x1 and w) and ˆˆs if  (x0 and w0). If r, x1 and w if , and ˆˆxw0 if . If r, then x1 and w for all . ˆAssume that A makes a take-it-or-leave-it offer t(r,,m)to S. We claim that one equilibrium is the no-collusion outcome, in which A offers the null side contract t(.,.,.)0 and S and A report truthfully. Suppose that , any undominated offer by A is rejected by S, who can get k by reporting r. Of course, it is not interim efficient. Note that there exists another equilibrium of the collusion game in which A makes a take-it-or-leave-it offer and which yields the CIE outcome. When  S reports  and S and A share . So, when parties to a coalition are asymmetrically informed, there may be multiple equilibria of the coalition formation game. Augmented revelation mechanism (which builds on Nash implementation) may not be needed if one insists on strong collusion proofness. An application to China 聂辉华、李金波，2006，《政企合谋与经济发展》，《经济学（季刊）》，第6卷第1期 聂辉华、蒋敏杰，2011，《政企合谋与矿难：来自省级面板数据的证据》，《经济研究》，第6期 Nie, Huihua, and Jinbo Li, 2012, “Collusion and Growth: A New Perspective on China Model”, Economic & Political Studies, forthcoming. 6