Changing the information structure between the agent and the supervisor, we consider a setting where the principal has no information about the supervisor and the agent does not know the type of supervisor when proposing a side contract. The supervisor may be seen as a perfect stranger to the firm. In this situation, we have to solve a problem of collusion with side payment under imperfect information.
When σ = θ ∈ Ω, what is the condition for a supervisor to conceal information ? If we denote by s(θ) the wage offered by the principal to the supervisor when the latter reports the observed signal and b(θ) the amount of covert transfer from the agent to the supervisor, the supervisor of type ψ accepts the side contract offered by the agent if and only if the net benefit expected from collusion is greater than the wage proposed by the principal. Thus, the following condition must hold for the covert transfer b(θ) :
b(θ) −ψ≥ s(θ) (16) In this setting, the type ψ of supervisor is unknown. We assume that the parameter ψ is the realization of a random variable characterized by the density function φ(ψ) and the distribution function Φ(ψ) on the support Ω = [0;1]. To get closed forms solutions, we further assume that the distribution function has the following form :
Φ(ψ) = 𝜓𝜖 (17) with 0 ≤ 𝜖 ≤ 1. Given the definition of Φ(ψ) and using (16), the probability that a coalition between the agent and the supervisor occurs may be expressed as :
Pr (ψ≤ b(θ) − s(θ)) = Φ(b(θ) − s(θ)) (18) where (b(θ)−s(θ)) indicates the surplus of the coalition. We note that the frequency of collusive behavior has a standard form in our problem. Indeed, the supervisor is more likely to accept a side contract from the agent when the latter offers a high value for the covert transfer.
Conversely, the probability of collusion is a decreasing function of the level of wage paid by the principal to the supervisor.
The agent maximizes the following net expected utility :
Max Φ(b(θ)−s(θ))[u(θ)−b(θ)] (19) Since the agent has no information about the type ψ of supervisor and since a truthful revelation by the supervisor to the principal lowers the agent's rent, the agent offers the following amount of covert transfer b(θ) to the supervisor given the distribution function :
Φ(ψ) = 𝜓𝜖 Proposition 7
Under asymmetric information, the optimal side transfer from the agent to the supervisor is given by the following amount:
𝑏 𝜃 = 𝜖
1+𝜖 𝑢 𝜃 + 1
1+𝜖 𝑠(𝜃)
With uncertainty about the type of supervisor, the agent proposes a side contract which induces the supervisor to misreport the signal to the principal. When the supervisor accepts the transaction with the agent, the optimal covert transfer is a linear combination of the rent u(θ) obtained by the agent and the wage s(θ) offered by the principal. The share of the agent's rent received by the supervisor is an increasing function of the fraction 𝜖
1+𝜖. This latter value corresponds to the mean level of the psychic cost ψ for the supervisor, since we have E(ψ) =
𝜖
1+𝜖. Since the probability of collusion is Pr(ψ ≤ b(θ) −s(θ)) and using the optimal covert transfer of proposition 7, we obtain the following equality 𝑏 𝜃 − 𝑠(𝜃) = 𝜖
1+𝜖( 𝑢 𝜃 − 𝑠(𝜃)) .
Corollary 3
Given the covert transfer, the optimal probability of collusion under asymmetric information is : Φ( 𝜖
1+𝜖( 𝑢 𝜃 − 𝑠(𝜃)) = 𝜖
1+𝜖( 𝑢 𝜃 − 𝑠(𝜃) 𝜖
Collusion between the two parties is more likely when the retention of information by the supervisor benefits the agent. It is an increasing function of the rent u(θ) since ∂Φ/∂u(θ) >
0. Besides, the probability of collusion is lowered by the level of salary offered by the principal to the supervisor, since the bribe becomes less attractive for the supervisor with
∂Φ/∂s(θ) < 0. An additional comment concerns the interpretation of , which is an indicator of the elasticity of collusion between the supervisor and the agent. In our framework, the monetary value of the agent's collusive activity is endogenous.
The parameter 𝜖 is equivalent to the shadow cost λ of the lateral side transfer for the agent as defined in Laffont and Tirole (1993, chapter 11), using the equivalence λ = 1/ 𝜖 . Since the probability of collusion may be expressed as Φ((u(θ)−s(θ))/ 1+λ ), we have lim λ→∞ Φ(.) = 0, meaning that an infinite shadow cost for the agent's transfer prevents from collusive behavior among a three-tier hierarchy.
Corollary 4
The Collusion proofness requires s(θ) = u(θ) ∀θ∈Ω.
Using corollary 3, it is easy to see that no collusion occurs when s(θ) = u(θ). So, what happens when the principal hires a nonfamily member as a supervisor? We remark that the collusion proofness is more costly since the equality s(θ) = u(θ) holds (∀θ ∈Ω).
This corresponds to a transfer of informational rent from the agent to the supervisor. As a consequence, it is in the interest for an ownership to include family members in the management of the corporation. While it is often argued that supervision by family members can be perceived as nepotism, we offer a different interpretation using the theory on incentives contracting. The rational of hiring supervisors among family members is simply the result of the reduced agency problem, in that it avoids collusive behaviors between supervisors and agents.
Proposition 8
The Collusion proofness in presence of a nonfamily supervisor requires the implementation of the following production allocation given by :
A mechanism that is robust to collusive behavior requires s(θ) = u(θ). Since the supervisor is not a family member, the principal is no longer characterized by an altruistic behavior towards the supervisor and thus β = 0.
We can now calculate the expected profit for the principal as follows :
𝐸Π= 1− 𝜁 𝑣 𝑞𝜃𝜃 𝜙 𝜃 − 𝑐 𝜃,𝑞𝜙 𝜃 − 𝑢(𝜃) 𝑑𝐹 𝜃 + 𝜁 𝑣 𝑞𝜃𝜃 𝜃 𝜃 −
𝑣′ 𝑞𝜙 𝜃 = 𝜕𝑐(𝜃,𝑞𝜙 𝜃 ) performance asked to the agent along all the interval Ω. The distortion whose amount is given by 1−𝜁𝜁 𝐹𝑓(𝜃)(𝜃)𝜕²𝑐 𝜃𝜕𝜃𝜕𝑞,𝑞𝜙(𝜃) 𝜃 does not depend on the altruism parameter β. Moreover, it prevails for all type θ ∈ Ω. Conversely, under perfect information about the supervisor, the degree of altruism alleviates the distortion. As a consequence, the presence of an outsider supervisor entails a lower degree of performance within the firm. A final comment is the interpretation of the solution given in proposition 8. The marginal benefit 𝑣′ 𝑞𝜙 𝜃 is equalized with the Thus, our analysis may be seen as a direct generalization of the results obtained by Laffont and Tirole (1993) on collusion in regulation policies contexts.
7 Conclusion
In this paper, we have attempted to embed altruism in the context of the firm theory. Our central assumption is that altruism operates only in family firms. Parents are especially generous to their children not only because they love them, but also because their own level of well-being would decline if they acted in any different way as demonstrated by Becker (1991). Conversely, altruism is not present in a non-family business organization, and the ownership of a firm is only concerned with the maximization of the firm's profit in that case.
Interestingly, non-family firms are often tempted to imitate family firms, in particular by promoting and 'producing' altruism through corporate culture (Hermalin, 2001). Our
contribution is to show what role information plays in the presence of altruism in such hierarchical models of production.
Specifically, we show how altruism influences agency relationships in family firms.
Altruism greatly helps to explain why the performance of family firms is often different from performance of other types of business organizations. Indeed, agency relationships are embedded in the strength of parent-child relationships. As pointed out by Pollak (1985), the main advantages of family governance are right incentives (claims on family resources), monitoring (owing to proximity), altruism and loyalty. Also, altruism compels parents to take care for their children and foster commitment to family firms. Specifically, this paper illustrates the claim of Simon (1993), according to whom altruism is expected to substantially change the theory of the firm.
Our results are two folds. On the one hand, we show that altruism only matters in a context of asymmetric information to determine the optimal production contract. Under symmetric information, no differences are expected between family and non-family firms, but the prevalent setting when dealing with production problems involves agency problems. On the other hand, we demonstrate that the issue of decentralization of information within a hierarchy matters when explaining the differential performances of the firms. Non-family firms have to devote more resources to the coordination of information within the hierarchical structure given the threat of collusion between members having relevant information. As a consequence, such private hierarchical firms would be less productive in terms of financial and innovation performances.
Finally, our analysis highlights the necessity to account jointly for social interactions within the firm and information aspects. So far, several studies have pointed out the role of altruism and trust both in the family and in the workplace (Mulligan, 1997, Rotemberg, 1994), but less attention has been devoted to their effects on the performance of firms. Our theoretical analysis, which is a contribution to the emerging formal literature on family business (Bhattacharya and Ravikumar, 2001, 2002, Chami, 2001) indicates that family ties may be good in terms of performance for the development of large firms. We believe that the expected positive impact of family altruistic relationships on the firm's performance is undoubtedly a central factor when explaining why family businesses are still the predominant form of business organization around the world.
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