Privacy and Team Incentives: Buffa, Liu & White (2025)

What this is. The core propositions and their economic logic from a pure theory paper on team contracting under private contracts, with an application to banking syndicates: enough to know what it proves and how, without reading all 55 pages. To replicate or extend it, read the full source at https://doi.org/10.1111/jofi.13496.

TL;DR

When compensation contracts are bilateral (observed only by the two parties who sign them), a principal contracting with two complementary-effort agents cannot commit to paying her agents enough: any promise of a high bonus to one agent can be secretly reneged on, and rational agents anticipate this, so equilibrium effort falls below the second-best (public-contracts) optimum. The paper shows that delegating contracting to the most skilled agent (the “Agent”) who then sub-contracts with the less skilled agent (the “Subagent”) partially solves this commitment problem via an observability effect: the Agent now observes the Subagent’s contract and so is not afraid of the principal reducing the Subagent’s incentives. The cost is a self-interest effect: the Agent skews the budget toward himself. Delegation dominates centralized private contracting when the project’s effort intensity $\rho = \theta/\gamma$ is above a threshold $\bar{\rho}(\alpha)$ that decreases with the skill gap $\alpha - 1/2$ between the agents. Applied to banking syndicates, the theory predicts when sole mandates, fee concentration, and hierarchical structures are optimal.

Core results

Magnitudes and significance are as reported (pure theory; all results are propositions or lemmas). Locators point into the source PDF.

#	Result	Locator	Magnitude / statement
R1	Under public contracts (second best), the optimal compensation budget equals effort intensity and the optimal allocation equals relative skill.	Proposition 1, p. 3453	$b^* = \rho,\; \phi^* = \alpha$ exactly; four structural parameters collapse to two: $\rho \equiv \theta/\gamma$ and $\alpha$.
R2	Under centralized private contracts, the budget is distorted downward and the allocation skewed toward the more skilled agent.	Proposition 2, p. 3456	$b^C = \rho - \frac{\alpha(1-\alpha)(2-\rho)\rho^2}{1-\alpha(1-\alpha)\rho^2} < b^*$; $\phi^C = \alpha + \frac{(\alpha-1/2)2\alpha(1-\alpha)\rho}{1-2\alpha(1-\alpha)\rho} \geq \alpha = \phi^*$. Distortions grow with $\alpha(1-\alpha)$ (skill heterogeneity) and $\rho$.
R3	Under delegated private contracts (principal contracts with one Agent, who sub-contracts), the budget distortion is smaller but the allocation distortion may be larger or smaller.	Proposition 3, p. 3460	$b^D = \rho - \alpha_A(1-\alpha_A)\rho^2 < b^*$; $\phi^D_A = \alpha_A + (1-\alpha_A)(1-\rho)$. Budget always closer to second best than under centralized: $b^C < b^D < b^*$ (Lemma 1).
R4	The principal prefers to delegate to the more skilled agent; delegation to the less skilled agent entails a larger allocation distortion that dominates.	Proposition 4, p. 3462	For any $\alpha > 1/2$, $v^D_{A=1} > v^D_{A=2}$, where $v^D_{A=i}$ is the principal’s expected payoff when agent $i$ is the Agent. The result follows because $g(\alpha,\Delta) > 1$ for all $\alpha \in (1/2,1)$ and $\Delta \in (0,1-\alpha)$ (Appendix eq. A11, p. 3489).
R5	Delegation dominates centralized contracting iff effort intensity is high enough: $\rho > \bar{\rho}(\alpha)$; it is also Pareto-improving iff $\rho > \tilde{\rho}(\alpha)$, with $1/2 < \tilde{\rho}(\alpha) < \bar{\rho}(\alpha) < 1/(2\alpha)$. Both thresholds decrease with $\alpha$.	Proposition 5, p. 3468; Figure 4, p. 3469	Delegation preferred when observability effect (from $\rho$ large) overcomes self-interest effect; delegation is Pareto-improving for a wider parameter region than where principal strictly prefers it.
R6	With partial transparency (agents observe each other’s contracts with probability $\lambda$), more transparency raises the compensation budget and reduces the skew toward the more skilled agent under centralized contracting but leaves the allocation unchanged under delegation. Delegation is optimal iff $\lambda < \bar{\lambda}$ for a unique threshold $\bar{\lambda} \in (0,1)$.	Proposition 6, pp. 3474-3475; Figure 5, p. 3476	$b^C(\lambda) = \rho - \frac{(1-\lambda)\alpha(1-\alpha)\rho^2(1-\rho)(2-\rho)}{(1-\rho)(1-\alpha(1-\alpha)\rho^2)+\lambda\alpha(1-\alpha)\rho^2(2-\rho)}$; $\phi^D_A(\lambda) = \alpha_A\rho + (1-\rho)$ (invariant in $\lambda$).
R7	When agents’ efforts are more substitutable (CES probability function with $\nu > 0$), the delegation region expands: sole mandates are more likely to be awarded as bank efforts become more substitutable.	Section IV.C, Figure 7, p. 3479	For baseline parameters $\alpha=0.75, \rho=0.55$: centralized contracting preferred when $\nu < 0.35$; delegation optimal for $\nu > 0.35$.

Overall (paper’s conclusion). With bilateral private contracts, the principal faces a credibility problem that distorts team incentives downward. Delegating contracting to the most skilled team member can restore efficiency when effort intensity is high. The theory delivers novel, testable predictions for banking syndicates: sole mandates (delegation) are more likely for firm-commitment deals, colder markets, less well-known issuers, larger skill gaps between underwriters, and when private compensation components are relatively more important.

Theory / model

The economic environment (Section I, p. 3448) has two dates and three risk-neutral players with limited liability. A principal hires two agents to implement a risky project. Agent $i = 1, 2$ exerts unobservable effort $e_i \geq 0$. Project output $X$ is Bernoulli (p. 3448, eq. 1):

$$X(e_1, e_2) = \begin{cases} 1 & \text{with prob. } \pi(e_1, e_2) \\ 0 & \text{with prob. } 1 - \pi(e_1, e_2) \end{cases} \tag{1}$$

The success probability follows a Cobb-Douglas team-effort function (p. 3449, eq. 2):

$$\pi(e_1, e_2) = \left(e_1^\alpha e_2^{1-\alpha}\right)^\theta \tag{2}$$

where $\theta > 0$ is the elasticity of expected output to team effort $e_1^\alpha e_2^{1-\alpha}$, and $\alpha \geq 1/2$ captures the relative skill of agent 1 (more skilled). The product $\alpha(1-\alpha)$ is an inverse measure of skill heterogeneity. The effort cost is (p. 3449, eq. 3):

$$c(e_i) = \kappa e_i^\gamma, \quad \kappa, \gamma > 0, \quad \gamma > \theta, \quad \kappa \geq 1 \tag{3}$$

The principal’s payoff (if the project succeeds) net of the total compensation budget $b$ is $v = (1-b)\pi(e_1,e_2)$ (p. 3451). Each agent’s payoff is expected compensation minus effort cost: $u_1 = \phi b (e_1^\alpha e_2^{1-\alpha})^\theta - \kappa e_1^\gamma$ and $u_2 = (1-\phi)b(e_1^\alpha e_2^{1-\alpha})^\theta - \kappa e_2^\gamma$.

The key ratio $\rho \equiv \theta/\gamma \in (0,1)$ captures effort intensity: how elastic expected output is to team effort, relative to the cost elasticity. Proposition 1 shows this is the only determinant of the optimal second-best compensation budget when contracts are public.

Two contracting schemes (Section III, p. 3454; Figure 1, p. 3450):

• Centralized contracting: principal offers contracts to both agents privately. Each agent observes only his own offer.
• Delegated contracting: principal offers a total budget $b$ to the Agent (the more skilled agent), who then sub-contracts with the Subagent. The Agent observes both contracts; the Subagent observes only his own offer.

Commitment problem. With public contracts, Proposition 1 establishes the second-best optimum $(b^*, \phi^*) = (\rho, \alpha)$ as the benchmark. When contracts are private, the principal can secretly renege on the promised high-incentive contract for one agent: agent $i$ cannot observe agent $j$‘s contract, so he cannot verify whether the indirect effort externality he expects is actually being provided. This destroys the indirect-incentive channel and depresses the equilibrium budget (Proposition 2, p. 3456).

Method

The paper’s method is theoretical (pure theory, no estimation). Equilibria are solved by backward induction in a two-period game, using the Perfect Bayesian Equilibrium (PBE) with passive beliefs (agents do not revise beliefs about the other agent’s effort when receiving an out-of-equilibrium offer, p. 3455). The solution procedure is:

1. Given the compensation budget $b$ and allocation $\phi$, solve each agent’s incentive-compatibility (IC) constraint for optimal effort (equations 4-5 in the public case, 10-12 in the centralized private case, 15-18 in the delegated case).
2. Impose equilibrium: each agent’s conjecture about the other’s effort equals the equilibrium effort level.
3. Solve the principal’s program for $(b^*, \phi^*)$ (or the Agent’s allocation program for $\phi_A^D$ in the delegated case).

The paper builds on principal-agent and promotion-contest frameworks. The key technical contribution is formalizing the observability effect vs. the self-interest effect of delegation, both deriving from the same bilateral-privacy assumption.

For the banking-syndicate application, the model is extended to partial transparency via a mixing parameter $\lambda \in [0,1]$ (Proposition 6, p. 3474): agents observe each other’s contracts with probability $\lambda$. The fully private and fully public cases are nested at $\lambda = 0$ and $\lambda = 1$ respectively. A CES probability function (eq. 33, p. 3478) $\pi(e_1,e_2) = (\alpha e_1^\nu + (1-\alpha)e_2^\nu)^\theta$ with substitutability parameter $\nu$ nests the Cobb-Douglas as $\nu \to 0^+$.

Empirical specifications

This is a pure theory paper; there is no econometric estimation. The paper’s empirical content is a set of qualitative comparative-statics predictions for banking syndicates (Section IV, pp. 3470-3482), which can be taken to data. The key mappings from model to data are:

• Degree of centralization / delegation: fraction of banks in the top tier of a syndicate hierarchy. More banks in the top tier = more centralized (the issuer deals directly with each rather than routing through a lead bank). A more concentrated distribution of underwriting fees (high HHI among top-tier banks) is an alternative delegation measure (p. 3471).
• Relative skill $\alpha$: proxied by standard underwriter reputation measures: Megginson and Weiss (1991) market-share rank; Carter and Manaster (1990) tombstone-based rank.
• Effort intensity $\rho$: harder-to-sell deals have higher $\rho$. Proxies include: firm-commitment vs. best-efforts underwriting; market “coldness” (volume of deals in the quarter); issuer credit quality / cash flows; issuer name recognition (p. 3472).
• Degree of transparency $\lambda$: higher when publicly-disclosed fees or spreads dominate compensation; lower when side benefits (e.g., future business from the issuer, allocation of underpriced shares) are a large share of total compensation (p. 3475).

Testable predictions from Propositions 5-6 and the CES extension:

1. Sole mandates (delegation) are more likely when the issue is firm-commitment, in colder markets, from less well-known issuers, and for lower-rated debt.
2. Fee income is more concentrated among a few top-tier banks when (a) underwriters’ skill is more asymmetric, (b) the deal is harder to place, and (c) private compensation components are relatively more important.
3. More pay transparency (higher $\lambda$) increases total underwriting spreads and reduces the share of the highest-reputation bank(s) under centralized (joint-mandate) structures.
4. Sole mandates become more likely as bank effort substitutability increases (CES result, Figure 7, p. 3479).

Datasets used

This is a theoretical paper. No dataset is used for estimation. The application to banking syndicates references the following empirical literature for operationalizing model parameters:

Reference / proxy	Role in paper	Wiki page
Megginson and Weiss (1991) underwriter reputation (market-share rank)	Proxy for relative skill $\alpha$ in syndicate application	No page yet
Carter and Manaster (1990) tombstone rank	Alternative proxy for relative skill $\alpha$	No page yet
Syndicate structure data (fraction of banks in top tier; HHI of fees)	Observable proxy for degree of delegation	No page yet

No quantitative empirical exercise is conducted in the paper itself.

Relation to prior work

The paper builds on several strands of the literature. Holmstrom (1982) establishes that public contracts with team moral hazard can in principle achieve first-best outcomes, which this paper uses as a conceptual benchmark (p. 3482). Segal (1999) analyzes the principal’s incentive to deviate from an efficient trade profile when contract offers are privately observed, and characterizes the optimal mechanism when agents’ messages to the principal can be made contingent on other agents’ messages; this paper complements that analysis by showing delegation can solve the commitment problem (p. 3483). Aghion and Tirole (1997) study a double-sided moral hazard problem where delegation encourages a single agent’s effort; the key difference here is that two agents’ efforts are complements and the principal makes no direct effort contribution, so delegation operates through a different channel (p. 3484).

On pay transparency, Halac et al. (2021) analyze a model where the principal can commit to the public distribution but keeps the realization of pay packages private, ruling out bad equilibria; their model differs in that the principal can commit to non-discriminatory pay, which she cannot in the present paper (p. 3481). Cullen and Pakzad-Hurson (2023) show that full pay transparency lowers pay inequality by reducing the principal’s bargaining power; this contrasts with the present paper’s finding that transparency raises pay levels and reduces inequality only when efforts are highly substitutable (p. 3481). DeMarzo and Kaniel (2023) build a model where agents have “keeping up with the Joneses” (KUJ) preferences and private contracts worsen externalities; in equilibrium agents’ KUJ preferences result in less negative optimal compensation on peer output, providing a rationale for “payment for luck” (p. 3484).

When to read the full paper

Read the original if you are: building a model of team contracting with private contracts; interested in the formal proofs of the propositions (Appendix pp. 3486-3494 and Internet Appendix); extending the theory to endogenous privacy, dynamic contracts, or more than two agents; or calibrating the banking-syndicate predictions to data (the comparative-statics section, IV.B, pp. 3475-3480 maps model parameters to observables). The Internet Appendix derives CES equilibria in full generality and provides robustness under non-passive beliefs.

Attribution and rights

Source: peer-reviewed, The Journal of Finance 80(6), December 2025, pp. 3443-3497. DOI: 10.1111/jofi.13496. Copyright 2025 the American Finance Association. This article is paywalled; no CC licence was found in Crossref metadata. This distillation is extract-only under fair-use principles: core results and equations reproduced for research commentary purposes. Distilled by an LLM (claude-sonnet-4-6) on 2026-06-03. Not human-verified. Not independently reproduced.

Buffa, Andrea M., Qing Liu, and Lucy White. “Privacy and Team Incentives.” The Journal of Finance 80, no. 6 (December 2025): 3443-3497. DOI: 10.1111/jofi.13496. Copyright 2025 the American Finance Association.