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arxiv: 2406.11712 · v5 · submitted 2024-06-17 · 💰 econ.TH

Incentive Contracts and Peer Effects in the Workplace

Marc Claveria-Mayol , Pau Mil\'an , Nicol\'as Oviedo-D\'avila This is my paper

Pith reviewed 2026-05-24 00:00 UTC · model grok-4.3

classification 💰 econ.TH
keywords incentive contractspeer effectsnetworkworkplaceoptimal designsubstitutabilitycomplementarityrisk
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The pith

Firms target steeper incentives at the most central workers in a peer network only when output risk is high enough, or at influencers of small isolated teams under complementarity.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper studies how firms set performance-based wages when workers' effort costs depend on colleagues through a fixed peer network. It derives the profit-maximizing assignment of incentive slopes under both substitutable and complementary production, and under full versus restricted discrimination across workers. A sympathetic reader cares because the results identify which positions in the network should receive the strongest pay-for-performance and quantify the profit penalty from uniform pay rules. The analysis also applies the network logic to questions of team structure and hiring.

Core claim

When effort is substitutable, the most central workers receive the steepest incentives only if output risk is sufficiently large; otherwise the firm favors workers whose influence is more local. When production is complementary across teams, stronger incentives go to workers who influence colleagues in small teams that themselves receive little influence from others. A sufficient network statistic measures the profit loss from having to pay workers of different centrality the same contract.

What carries the argument

The peer network through which effort costs depend on colleagues and through which performance incentives cascade to affect the whole organization.

If this is right

  • Under substitutability and low risk, optimal contracts favor workers closer to those they influence rather than the globally most central.
  • Under complementarity, optimal contracts assign stronger incentives to workers who affect small, low-influence teams.
  • A single network statistic is enough to calculate the profit loss when the firm must use the same contract for workers of varying centrality.
  • The same network logic guides choices of firm structure and workforce investments.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Firms may want to reshape team boundaries or hiring to alter the network positions that receive the highest-powered incentives.
  • In low-risk environments the results favor building organizations around local influence clusters rather than high-centrality hubs.

Load-bearing premise

The structure of the peer network linking effort costs is known to the firm and fixed at the time contracts are chosen.

What would settle it

Measure whether, in high-risk settings with substitutable effort, incentive slopes rise with network centrality while in low-risk settings they rise instead with local closeness to influenced colleagues.

Figures

Figures reproduced from arXiv: 2406.11712 by Marc Claveria-Mayol, Nicol\'as Oviedo-D\'avila, Pau Mil\'an.

Figure 1
Figure 1. Figure 1: Performance pay and overall wage distribution for two different organizational [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: A directed network with 5 agents. common influence worker i shares with j: wij > 0 if i and j jointly influence a third worker, or if i shares common influence with someone who shares common influence with j, and so on along chains of any length.21 Example 1 (Chains of Common Influences). Consider the network in [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Substitutes: Workers i and j both have incentive paths lead￾ing to worker s. This means that raising αi increases the marginal cost of αj . s i ℓ j ∂es ∂αi > 0 ∂eℓ ∂αj > 0 [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: In the supermarket chain network from Mas and Moretti (2009) it can pay off (if risk is low) to incentivize nodes in the middle more than nodes on the left, even though nodes on the left are more central. cancel each other out, yielding α2 = 1 1 + rσ2 . Interestingly, since the network effects exactly cancel, worker 2 ens up receiving the textbook￾level of incentives for the standard textbook case with no … view at source ↗
Figure 6
Figure 6. Figure 6: Panel A: Positive peer effects (i.e., λ > 0); Panel B: Negative peer effects (i.e., λ < 0). The size of the node represents their Bonacich centrality and the color represents the allocation of incentives (red being most incentives and blue being least). Recent work by Galeotti et al. (2020) shows that when λ < 0, optimal interventions alternate incentives between adjacent individuals due to convex costs. T… view at source ↗
Figure 7
Figure 7. Figure 7: Panel A: Within-group variance is zero. No surplus loss. Panel B: Within-group variance is 0.53. Surplus loss, following Proposition 5, is about 0.85. T and group assignment Te is given by: ∆STe−T = 1 2 1 ′ (eTe − eT). The following result focuses on ∆SI−T, which corresponds to the loss of surplus when groups are assigned by T, relative to fully personalized contracts, I. We show that the efficiency loss c… view at source ↗
Figure 8
Figure 8. Figure 8: The loss of surplus ∆SI−T is increasing in within-group variance in centrality. The relationship is approximately linear and becomes deterministic as σ 2 increases. exact linear relationship as σ 2 grows. Thus, while proportionality holds strictly only in the limit, the efficiency cost of coarse contracts is well captured by this simple statistic. 4 Modular Production So far, we have assumed output is a li… view at source ↗
Figure 9
Figure 9. Figure 9: Modular shares, µk, and incentives, αi , in four different firm configurations. Each firm has a 4-worker and 6-worker module. (parameters: λ = 0.15 and rσ2 = 1). belongs to: MBαi = X j ∂ej ∂αi µk(j) . Stacking these up across all workers, you get the vector of marginal benefits which is precisely the new centrality measure C′µ in equation (14). The values of µk (which must sum to 1) are determined by modul… view at source ↗
Figure 10
Figure 10. Figure 10: Performance-pay for Different Modular Configurations. Simulations are run for [PITH_FULL_IMAGE:figures/full_fig_p029_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: A line network with 7 workers. 1 and 3, i.e., SEα1 and SEα3 : SEα1 = α1 [PITH_FULL_IMAGE:figures/full_fig_p050_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Modular share, µk, for the planted partition model with linking parameters p and q. Two equal-sized modules (blue line) and the asymmetric case with two modules of sizes 8 workers (green line) and 12 workers (red line) (parameters: λ = 0.025, σ 2 = 1 and r = 1). We consider the example of a firm with N = 20 workers and K = 2 modules and look at two different cases: equal module sizes (i.e., 10 workers in … view at source ↗
Figure 13
Figure 13. Figure 13: Complete Bipartite graphs with N = 10. An asymmetric bipartite graph (left panel) generates lower profits than a symmetric one (right panel). Consider all networks with a degree distribution that follows a power law P(d) ∼ d −γ . Intuitively, as γ increases both µ1 and Var(u1) in equation (16) increase because the dis￾tribution puts more weight on the right tail, creating dominant workers with much larger… view at source ↗
Figure 14
Figure 14. Figure 14: All 2-regular graphs with N = 10 give the same profits. m: 2E(π ⋆ )bipartite = ( √ m + √ n) 2 /2 (1 + rσ2 )(1 − λ √ nm) 2 − (λ √ nm) 2 + ( √ m − √ n) 2 /2 (1 + rσ2 )(1 + λ √ nm) 2 − (λ √ nm) 2 . From this, we identify the profit-maximizing structure among all complete bipartite graphs: Corollary 4 (Complete Bipartite Networks). Among all complete bipartite graphs with n nodes in group A and m nodes in gro… view at source ↗
Figure 15
Figure 15. Figure 15: Planted Partition model with n = 10 and p + q = 0.8. Panel A: p = q = 0.4. Panel B: p = 0.6, q = 0.2. Panel C: p = 0.75, q = 0.05. Proposition 8, where p represents the probability of within-group connections and q the probability of cross-group connections. While p + q determines overall connectivity, ho￾mophily is captured by the ratio p/q. Using Proposition 9 and the expected adjacency matrix G¯ ∈ {p, … view at source ↗
Figure 16
Figure 16. Figure 16: Two directed networks with 5 workers: (a) a directed cycle and (b) a regular [PITH_FULL_IMAGE:figures/full_fig_p061_16.png] view at source ↗
read the original abstract

We analyze how firms should design wage contracts when workers collaborate in teams and effort costs depend on colleagues through a peer network. Performance-based compensation generates incentives that cascade through the organization, which firms target to boost profits. We analyze optimal incentive design if firms can -- and can't -- fully discriminate across workers, and when the production technology is separable or complementary across divisions. When workers' effort is substitutable, the most central workers -- those who influence most colleagues directly and indirectly -- receive the steepest incentives only when output risk is sufficiently large; otherwise firms prioritize workers who are closer to those they influence. When production technology exhibits complementarity across teams, stronger incentives are assigned to workers who influence colleagues in small teams that receive little influence from others. We derive a sufficient network statistic that measures the profit loss when firms must compensate workers of varying centrality equally. Finally, we apply our findings to organizational design questions, such as optimal firm structure and workforce investments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The paper analyzes optimal incentive contracts when workers' effort costs depend on colleagues via a known, fixed peer network. It derives results for both fully discriminating and non-discriminating firms, under separable (substitutable) and complementary production technologies. For substitutable efforts, most-central workers receive the steepest incentives only when output risk is sufficiently large; otherwise proximity to influenced workers is prioritized. Under complementarity, stronger incentives target workers who influence colleagues in small teams receiving little incoming influence. A sufficient network statistic is provided for the profit loss from equal compensation across centrality levels, with applications to firm structure and workforce investment.

Significance. If the derivations hold, the paper supplies a clean theoretical framework linking network centrality measures to targeted incentive slopes, with explicit risk and team-size thresholds that distinguish substitutability from complementarity. The sufficient statistic for equal-compensation losses is a portable, falsifiable object that could support empirical work. The explicit statement that the network is known and fixed at contracting time makes the scope of the results transparent rather than hidden.

minor comments (3)
  1. The abstract states the maintained assumption that the adjacency structure is known to the firm and exogenous at contract time; the stress-test concern therefore does not apply as an unstated restriction.
  2. Notation for the network adjacency matrix, centrality vector, and the risk parameter should be introduced with a single consolidated table or definition block early in the model section to aid readability.
  3. The organizational-design applications in the final section would benefit from one or two concrete numerical examples (e.g., a small star network versus a line) showing how the sufficient statistic changes with firm structure.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive and accurate summary of our paper, as well as for recommending minor revision. The referee's description correctly captures the key results on optimal incentive design under substitutability and complementarity, the role of network centrality, and the sufficient statistic for equal-pay losses. No specific major comments or requested changes were provided in the report.

Circularity Check

0 steps flagged

No circularity; derivation self-contained in theoretical model

full rationale

The provided abstract and description outline a standard theoretical model in which optimal incentive contracts are derived from explicit assumptions about peer networks, effort substitutability/complementarity, and risk. No quoted steps reduce by construction to fitted parameters renamed as predictions, self-definitional relations, or load-bearing self-citations. The central claims (e.g., centrality-based targeting conditional on risk) are presented as model outputs rather than tautological inputs, and the network structure is treated as an exogenous known input rather than derived from the results themselves. This is the expected non-finding for a pure theory paper with no empirical fitting or circular self-reference.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no equations or sections from which to extract specific free parameters, axioms, or invented entities; the central modeling choice is the peer-network dependence of effort costs.

pith-pipeline@v0.9.0 · 5694 in / 1128 out tokens · 23557 ms · 2026-05-24T00:00:22.307130+00:00 · methodology

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Reference graph

Works this paper leans on

27 extracted references · 27 canonical work pages

  1. [1]

    Mobius, and A

    Ambrus, A., M. Mobius, and A. Szeidl (2014): Consumption Risk-Sharing in Social Networks, The American Economic Review, 104, 149--182

    work page 2014

  2. [2]

    Ashraf, N. and O. Bandiera (2018): Social incentives in organizations, Annual Review of Economics, 10, 439--463

    work page 2018

  3. [3]

    Calv \'o -Armengol, and Y

    Ballester, C., A. Calv \'o -Armengol, and Y. Zenou (2006): Who's who in networks. Wanted: The key player, Econometrica, 74, 1403--1417

    work page 2006

  4. [4]

    Barankay, and I

    Bandiera, O., I. Barankay, and I. Rasul (2005): Social Preferences and the Response to Incentives: Evidence from Personnel Data, The Quarterly Journal of Economics, 120, 917--962

    work page 2005

  5. [5]

    Bloch, F., M. O. Jackson, and P. Tebaldi (2023): Centrality measures in networks, Social Choice and Welfare, 61, 413--453

    work page 2023

  6. [6]

    Bolton, P. and M. Dewatripont (2004): Contract theory, MIT press

    work page 2004

  7. [7]

    Bramoull \'e , Y. and R. Kranton (2007): Public goods in networks, Journal of Economic Theory, 135, 478--494

    work page 2007

  8. [8]

    Patacchini, and Y

    Calv \'o -Armengol, A., E. Patacchini, and Y. Zenou (2009): Peer effects and social networks in education, The Review of Economic Studies, 76, 1239--1267

    work page 2009

  9. [9]

    (2015): Robustness and Linear Contracts, The American Economic Review, 105, 536--563

    Carroll, G. (2015): Robustness and Linear Contracts, The American Economic Review, 105, 536--563

    work page 2015

  10. [10]

    (2024): Moral Hazard with Network Effects, Working Paper

    Claveria-Mayol, M. (2024): Moral Hazard with Network Effects, Working Paper

    work page 2024

  11. [11]

    Dustmann, and U

    Cornelissen, T., C. Dustmann, and U. Sch \"o nberg (2017): Peer Effects in the Workplace, American Economic Review, 107, 425--456

    work page 2017

  12. [12]

    Golub, and A

    Dasaratha, K., B. Golub, and A. Shah (2023): Equity Pay in Networked Teams, Available at SSRN 4452640

    work page 2023

  13. [13]

    Frenkel, S. J. (2003): The embedded character of workplace relations, Work and Occupations, 30, 135--153

    work page 2003

  14. [14]

    Golub, and S

    Galeotti, A., B. Golub, and S. Goyal (2020): Targeting interventions in networks, Econometrica, 88, 2445--2471

    work page 2020

  15. [15]

    Hamilton, B., J. A. Nickerson, and H. Owan (2003): Team Incentives and Worker Heterogeneity: An Empirical Analysis of the Impact of Teams on Productivity and Participation, Journal of Political Economy, 111, 465--497

    work page 2003

  16. [16]

    (1982): Moral hazard in teams, The Bell journal of economics, 324--340

    Holmstrom, B. (1982): Moral hazard in teams, The Bell journal of economics, 324--340

    work page 1982

  17. [17]

    Holmstrom, B. and P. Milgrom (1987): Aggregation and Linearity in the Provision of Intertemporal Incentives, Econometrica, 55, 303--328

    work page 1987

  18. [18]

    --- -.1pt --- -.1pt --- (1991): Multitask Principal-Agent Analyses: Incentive Contracts, Asset Ownership, and Job Design, Journal of Law, Economics, & Organization, 7, 24--52

    work page 1991

  19. [19]

    Macho-Stadler, I. and D. P \'e rez-Castrillo (1993): Moral hazard with several agents: The gains from cooperation, International Journal of Industrial Organization, 11, 73--100

    work page 1993

  20. [20]

    --- -.1pt --- -.1pt --- (2016): Moral Hazard: Base Models and Two Extensions, CESifo Working Paper Series

    work page 2016

  21. [21]

    Mas, A. and E. Moretti (2009): Peers at work, American Economic Review, 99, 112--145

    work page 2009

  22. [22]

    Powell, and B

    Matouschek, N., M. Powell, and B. Reich (2023): Organizing Modular Production,

    work page 2023

  23. [23]

    Mil\' a n, P. and N. Oviedo-D\' a vila (April, 2024): Incentive contracts and peer effects in the workplace, BSE Working Paper

    work page 2024

  24. [24]

    Mirrlees, J. A. (1999): The Theory of Moral Hazard and Unobservable Behaviour, The Review of Economic Studies, 66, 3--21

    work page 1999

  25. [25]

    (1984): Optimal Incentive Schemes with Many Agents, The Review of Economic Studies, 51, 433--446

    Mookherjee, D. (1984): Optimal Incentive Schemes with Many Agents, The Review of Economic Studies, 51, 433--446

    work page 1984

  26. [26]

    Parise, F. and A. Ozdaglar (2023): Graphon games: A statistical framework for network games and interventions, Econometrica, 91, 191--225

    work page 2023

  27. [27]

    (2022): Optimal compensation scheme in networked organizations, in Optimal compensation scheme in networked organizations: Shi, Xiangyu, [Sl]: SSRN

    Shi, X. (2022): Optimal compensation scheme in networked organizations, in Optimal compensation scheme in networked organizations: Shi, Xiangyu, [Sl]: SSRN

    work page 2022