Pith. sign in

REVIEW 3 major objections 5 minor 51 references

Optimal evaluation deliberately distorts away from true output

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Optimal organizational evaluation rules deliberately distort from true output, pairing with positive or negative assortative assignment depending on whether non-discretionary advantage or effort matters more for production.

T0 review reviewed 2026-07-09 challenge →

load-bearing objection Solid theory of joint evaluation-and-assignment design; the interior-equilibrium assumption is load-bearing but the paper is honest about it. the 3 major comments →

arxiv 2607.07280 v1 pith:HU3EG5AE submitted 2026-07-08 econ.TH

Evaluation and Assignment with Networked Competition and Spillovers

Antonio Cabrales , Wenhao Cheng This is my paper
classification econ.TH
keywords relative performance evaluationworker assignmentorganizational designincentivescontestsnetwork gamespeer effectsspillovers
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

This paper studies how an organization should jointly design two things: the rule used to evaluate workers' performance, and the assignment of workers to positions. Workers compete against peers linked by a competition network, while their non-discretionary advantages (talent, mentoring, reputation) propagate through a separate spillover network. The planner maximizes true output, which depends on both effort and advantage, but gets to choose an evaluation rule that can deliberately over- or under-weight effort relative to advantage. The central result is that the optimal evaluation rule almost never coincides with true output. When effort matters more for output, the planner should underweight effort in evaluation and assign high-ability workers to low-spillover positions (negative assortative assignment), creating disadvantage that drives agents to work harder. When advantage matters more for output, the planner should overweight effort in evaluation and assign high-ability workers to high-spillover positions (positive assortative assignment), exploiting spillovers while preventing advantaged agents from coasting. The cutoff between these two regimes depends on the intensity of competition: denser benchmarking networks push the planner toward the incentive-generating negative-sorting regime.

Core claim

The paper's central mechanism is a complementarity between evaluation distortion and assignment sorting. The planner's objective decomposes into a term depending on total effort (driven by the evaluation weight and Katz-Bonacich centrality in the competition network) and a term depending on total effective advantage (driven by the assignment and the spillover network). Because equilibrium effort is decreasing in effective advantage, the planner can use assignment as an effort-inducing instrument: minimizing total advantage creates disadvantaged agents who compensate through harder work. The evaluation weight controls how strongly advantage depresses effort, so the planner tunes it jointly. A

What carries the argument

The model uses two networks: a competition network W governing benchmarking comparisons, and a spillover network M governing how fixed types propagate. Equilibrium effort takes a closed form involving Katz-Bonacich centrality q = (I - beta W)^{-1} 1 of the competition network and the spillover-weighted type vector. The planner's problem reduces to maximizing a one-dimensional criterion in the assignment, with the sign of (1 - s/omega) determining whether to maximize or minimize total effective advantage. A cutoff s* separates the positive-assortative regime from the negative-assortative regime. Under pairwise stability with transferable utility and symmetric M, stable assignments sort by the

Load-bearing premise

The model assumes that for all relevant evaluation weights, assignments, and positions, every agent's non-discretionary advantage falls in a range ensuring they all exert strictly positive effort in equilibrium. If advantage is too extreme, some agents give up entirely, the closed-form effort expression breaks down, and the planner's optimization results no longer hold.

What would settle it

If in real organizations the non-discretionary advantage distribution is highly dispersed (some workers have overwhelming advantages or severe disadvantages), corner equilibria with zero-effort agents would arise, invalidating the closed-form characterization and the clean sorting predictions.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Organizations with denser peer-comparison networks should be more likely to use negative assortative assignment, placing talented workers in less connected roles to create effort incentives.
  • Reforms that increase the weight on effort in evaluation should raise effort disproportionately among workers who previously enjoyed large non-discretionary advantages.
  • When workers can privately swap tasks, observed assignment sorting reflects private positional advantage rather than the organization's spillover objective, creating a measurable wedge between decentralized and optimal assignment.
  • The output loss from decentralized assignment constraints decreases with competition intensity when the first best uses positive assortative assignment, but increases when the first best uses negative assortative assignment.
  • The sign of assortative matching between worker ability and position spillover centrality should flip depending on whether the evaluation rule overweights or underweights effort relative to true production technology.

Where Pith is reading between the lines

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

  • The model implies that organizations using forced-ranking or calibration systems with many comparison links should exhibit different assignment patterns than those with sparse benchmarking, even holding worker quality fixed.
  • If the spillover network were endogenous to agent behavior (e.g., agents choosing to interact less with direct competitors), the planner's optimal evaluation weight would likely shift further from true output to compensate for the reduced spillover channel.
  • The framework could extend to dynamic settings where assignment affects learning and type evolution, potentially creating a path-dependence where early assignments lock in advantage distributions that future evaluation rules must accommodate.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This paper studies the joint design of evaluation rules and worker assignment in an organization where performance depends on both effort and non-discretionary advantage. Agents are linked by two networks: a competition structure W governing benchmarking comparisons, and a spillover structure M governing how fixed types propagate into effective advantage. The planner chooses an assignment m and an evaluation weight omega to maximize total output, which depends on effort and advantage with weight s. In Stage 2, agents exert effort in a network contest. The main results characterize equilibrium effort (Proposition 1), the planner's optimal policy (Proposition 3), and the output loss from requiring pairwise stable assignments (Proposition 5). The key finding is that the optimal evaluation rule generally differs from true output: when effort is more important in production (s > s*), the planner lowers omega and uses negative assortative assignment; when advantage is more important (s < s*), the planner raises omega and uses positive assortative assignment. The paper also shows that stability loss depends on competition intensity Q, decreasing in Q when the first-best is positive assortative and increasing when it is negative assortative.

Significance. The paper makes a genuine contribution by jointly studying evaluation design and assignment in a networked environment with two distinct network structures. The separation of competition and spillover networks is conceptually valuable and distinguishes the model from prior work on contests on networks or assignment models alone. The closed-form equilibrium effort expression in Proposition 1, linking effort to Katz-Bonacich centrality and effective advantage, is clean and generates testable comparative statics. The main policy result—that the planner deliberately distorts evaluation away from true output and that the direction of distortion flips with the relative importance of effort—is non-obvious and well-motivated. The pairwise stability extension (Section 4) adds practical relevance by showing how decentralized assignment constraints create a measurable output loss. The full proofs in the appendix are detailed and the model is self-contained with exogenous parameters.

major comments (3)
  1. Assumption 2 (Interior-equilibrium region, Section 3.1) requires that for every omega in [omega_I, 1], every assignment m, and every position j, the non-discretionary component lies in a specific interval. This uniformity over all assignments is load-bearing because Proposition 1 and all downstream results depend on the closed-form all-active equilibrium. The concern is that the assumption is most binding exactly at the assignments the planner most wants to implement: when s > s*, the planner chooses negative assortative assignment, which creates the most uneven effective-advantage profile. The paper should explicitly discuss whether Assumption 2 is compatible with the negative assortative regime it characterizes, or provide a parameterized example showing that both can hold simultaneously in a non-trivial case.
  2. Appendix A.6 provides two sufficient conditions (Propositions A.1 and A.2) under which restricting omega to [omega_I, 1] is without loss. However, these conditions are themselves demanding. Proposition A.1 requires Xi >= tau_I, which demands that every possible active subset has enough own effective advantage relative to competition pressure. The paper would benefit from either (a) a concrete numerical example verifying these conditions in a setting with non-trivial type heterogeneity and spillover inequality, or (b) a more transparent discussion of what economic restrictions these conditions impose and how binding they are in practice.
  3. Proposition 3 characterizes the optimal policy with three cases and a cutoff s*. The cutoff formula involves eT_minus and eT_plus, which themselves depend on whether the stationary points b_omega(B) are interior or at boundary values. The resulting case structure is correct but difficult to parse. A simpler statement of the main economic intuition—perhaps through a proposition stating only the interior case under Assumption 3—would help readers separate the economic content from the technical case enumeration.
minor comments (5)
  1. The notation omega_hat(B) in the main text (e.g., around Equation 3.9) and b_omega(B) in the appendix are used interchangeably; standardizing would improve readability.
  2. In Example 1 (Section 3.2), the spillover matrix M^S = I + W^S is introduced but the economic interpretation of this specific functional form is not discussed. A brief note on why this is a natural spillover structure would help.
  3. The paper references 'Katz-Bonacich centrality' in the abstract but 'Katz centrality' in the body (Section 3.1). Consistent terminology would be preferable.
  4. Equation (2.9) and the surrounding discussion could more explicitly state that the normalization of weights summing to one is a modeling choice and briefly note the consequence of relaxing it, rather than relegating this to a footnote.
  5. The empirical implications discussed in Section 3.2 are valuable but somewhat scattered across the text. Consolidating them into a dedicated subsection or a summary table would increase their visibility.

Circularity Check

0 steps flagged

No circularity: derivation chain is self-contained with exogenous primitives and FOC-derived results

full rationale

The paper's derivation chain is entirely self-contained. All model parameters (s, ω, β, W, M, a_i, σ, U, v) are exogenous primitives, not fitted to data. The equilibrium effort (Proposition 1) is derived from standard contest first-order conditions. The planner's objective reduction (Lemma 2) is pure algebraic substitution of equilibrium effort into the output function. The optimal assignment (Proposition 2) follows from the rearrangement inequality applied to b^T a(m). The cutoff s* (Proposition 3) is derived from comparing branch values at their FOC-determined stationary points, not postulated or fitted. The stability results (Propositions 4-5) follow from swap-gain analysis and monotonicity of derived functions. No self-citations by the current authors are load-bearing: all foundational references (König et al. 2017, Ballester et al. 2006, Lazear and Rosen 1981, etc.) are to external work. No 'prediction' reduces to a fitted input by construction. The skeptic's concern about Assumption 2's restrictiveness is a valid scope/robustness concern but is not a circularity issue—the paper is transparent that results hold within stated assumptions, and the assumptions do not encode the conclusions.

Axiom & Free-Parameter Ledger

7 free parameters · 7 axioms · 3 invented entities

The model has 7 exogenous parameters, none fitted to data. The three key assumptions (1-3) are standard to domain-specific, with Assumptions 2 and 3 being somewhat restrictive to ensure interior equilibria. The invented entities (W, M, θ) are modeling constructs with stated empirical counterparts but no empirical validation in the paper.

free parameters (7)
  • ω (evaluation weight)
    Chosen by the planner as a decision variable; not fitted to data.
  • s (true output effort weight)
    Exogenous parameter describing production technology.
  • β (competition intensity)
    Exogenous parameter scaling the competition network.
  • α (common advantage shifter)
    Exogenous organization-wide constant.
  • v (marginal cost of effort)
    Exogenous cost parameter.
  • U (prize value)
    Exogenous reward parameter.
  • σ (noise standard deviation)
    Exogenous noise parameter in success probability.
axioms (7)
  • domain assumption Assumption 1: 0 ≤ β < 1/ρ(W) (network stability)
    Standard in network games; ensures (I - βW) is invertible and equilibrium does not explode. Invoked in Section 3.1.
  • ad hoc to paper Assumption 2: Interior-equilibrium region exists for ω ∈ [ω_I, 1]
    Restricts non-discretionary component to an interval ensuring all agents exert positive effort and do not deviate to zero. Invoked in Section 3.1; load-bearing for Proposition 1 and all downstream results.
  • ad hoc to paper Assumption 3: Aggregate non-discretionary component bounded
    Ensures interior candidate evaluation weights satisfy ω_I ≤ b̂ω(B−) ≤ b̂ω(B+) ≤ 1. Invoked in Section 3.2; simplifies Proposition 3 to the interior case.
  • domain assumption Linear production and evaluation functions (Equations 2.1, 2.8)
    Output and evaluation scores are linear in effort and effective advantage. Standard in personnel economics (Prendergast 1999). Invoked in Section 2.
  • domain assumption Normal noise in success probability (u_j ~ N(0, σ²))
    Probit-style contest success function. Invoked in Equation 2.4.
  • domain assumption Symmetric spillover matrix M (for stability analysis)
    M_jk = M_kj assumed for pairwise stability characterization. Invoked in Section 4.1.
  • domain assumption Transferable utility for pairwise swaps
    Swaps implemented when total pair payoff increases. Invoked in Section 4.1.
invented entities (3)
  • Competition structure W no independent evidence
    purpose: Network determining which positions are benchmarked against each other in evaluation.
    Modeling construct; the paper notes it can be constructed from observable benchmarking patterns (Section 2.2).
  • Spillover structure M no independent evidence
    purpose: Matrix determining how agent types propagate into effective advantage across positions.
    Modeling construct; the paper notes it can be constructed from observable channels like co-location or mentoring links (Section 2.1).
  • Effective advantage θ(m) = Ma(m) no independent evidence
    purpose: Position-specific non-discretionary advantage combining own type and spillovers.
    Derived construct from M and agent types; not independently measured in the paper.

reviewed 2026-07-09 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Evaluation and Assignment with Networked Competition and Spillovers." pith.science (2026). https://pith.science/paper/HU3EG5AE

@misc{pith2026260707280,
  author       = {Pith},
  title        = {Pith review of: Evaluation and Assignment with Networked Competition and Spillovers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HU3EG5AE}},
  note         = {Machine review of arXiv:2607.07280}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

This paper studies how organizations should jointly design evaluation rules and assign workers when performance depends on both effort and non-discretionary advantage. Agents choose effort in positions linked by a competition network, while their effective advantage depends on own type and spillovers through a second network. The planner chooses both the assignment and the effort weight in evaluation. Equilibrium effort rises with a position's Katz-Bonacich centrality and falls with effective advantage. The optimal evaluation rule generally differs from true output. When effort is more important in production, the planner lowers the effort weight and uses negative assortative assignment to strengthen incentives. When advantage is more important, the planner raises the effort weight and uses positive assortative assignment to exploit spillovers. We also study a constraint requiring assignments to be pairwise stable, which creates an output loss depending on the intensity of competition.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

51 extracted references · 51 canonical work pages · 1 internal anchor

  1. [1]

    Wanted: The key player , author=

    Who's who in networks. Wanted: The key player , author=. Econometrica , volume=. 2006 , publisher=

    work page 2006

  2. [2]

    Econometrica , volume=

    Networks in conflict: Theory and evidence from the great war of africa , author=. Econometrica , volume=. 2017 , publisher=

    work page 2017

  3. [3]

    1944 , publisher =

    von Neumann, John and Morgenstern, Oskar , title =. 1944 , publisher =

    work page 1944

  4. [4]

    , title =

    Shapley, Lloyd S. , title =. Contributions to the Theory of Games II , editor =

    work page

  5. [5]

    , title =

    Gillies, Donald B. , title =. Contributions to the Theory of Games IV , editor =

    work page

  6. [6]

    , title =

    Bloch, Francis and Jackson, Matthew O. , title =. Journal of Economic Theory , volume =. 2007 , doi =

    work page 2007

  7. [7]

    Journal of Economic Literature , volume=

    The provision of incentives in firms , author=. Journal of Economic Literature , volume=. 1999 , publisher=

    work page 1999

  8. [8]

    Review of Economic Studies , volume =

    A Continuous-Time Version of the Principal--Agent Problem , author =. Review of Economic Studies , volume =. 2008 , publisher =

    work page 2008

  9. [9]

    Annual Review of Economics , year =

    Besley, Timothy and Burgess, Robin and Khan, Adnan and Xu, Guo , title =. Annual Review of Economics , year =

    work page

  10. [10]

    Perceived Competition in Networks , author=

    work page

  11. [11]

    Economic Theory , volume=

    Contests on networks , author=. Economic Theory , volume=. 2024 , publisher=

    work page 2024

  12. [12]

    Journal of Economic Behavior & Organization , volume=

    A contest success function for networks , author=. Journal of Economic Behavior & Organization , volume=. 2018 , publisher=

    work page 2018

  13. [13]

    Journal of Economic Theory , year =

    Fleckinger, Pierre , title =. Journal of Economic Theory , year =

    work page

  14. [14]

    and Ku, Hyejin and Salvanes, Kjell G

    Johnsen, Julian V. and Ku, Hyejin and Salvanes, Kjell G. , title =. The Review of Economic Studies , year =

    work page

  15. [15]

    and Williams, Joan C

    Khan, Raafiya Ali and Korn, Rachel M. and Williams, Joan C. , title =. Harvard Business Review , year =

    work page

  16. [16]

    Journal of Accounting Research , year =

    Cardinaels, Eddy and Feichter, Charlotta , title =. Journal of Accounting Research , year =

    work page

  17. [17]

    and Stokey, Nancy L

    Green, Jerry R. and Stokey, Nancy L. , title =. Journal of Political Economy , year =

    work page

  18. [18]

    and Stiglitz, Joseph E

    Nalebuff, Barry J. and Stiglitz, Joseph E. , title =. The Bell Journal of Economics , year =

    work page

  19. [19]

    The Review of Economic Studies , year =

    Mookherjee, Dilip , title =. The Review of Economic Studies , year =

    work page

  20. [20]

    , title =

    Dye, Ronald A. , title =. Journal of Accounting Research , year =

    work page

  21. [21]

    The Review of Economic Studies , year =

    Maskin, Eric and Qian, Yingyi and Xu, Chenggang , title =. The Review of Economic Studies , year =

    work page

  22. [22]

    Relative Performance or Team Evaluation? Optimal Contracts for Other-Regarding Agents , journal =

    Bartling, Bj. Relative Performance or Team Evaluation? Optimal Contracts for Other-Regarding Agents , journal =. 2011 , volume =

    work page 2011

  23. [23]

    The Review of Economic Studies , year =

    Ozdenoren, Emre and Yuan, Kathy , title =. The Review of Economic Studies , year =

    work page

  24. [24]

    Games and Economic Behavior , year =

    Sun, Yang and Zhao, Wei , title =. Games and Economic Behavior , year =

    work page

  25. [25]

    Peer Effects and Incentives , journal =

    Kr. Peer Effects and Incentives , journal =. 2016 , volume =

    work page 2016

  26. [26]

    Bochet, Olivier and Faure, Mathieu and Long, Yan and Zenou, Yves , title =

    work page

  27. [27]

    Journal of Economic Literature , year =

    Sattinger, Michael , title =. Journal of Economic Literature , year =

    work page

  28. [28]

    and Murphy, Kevin M

    Becker, Gary S. and Murphy, Kevin M. , title =. The Quarterly Journal of Economics , year =

    work page

  29. [29]

    Journal of Political Economy , year =

    Garicano, Luis , title =. Journal of Political Economy , year =

    work page

  30. [30]

    The Quarterly Journal of Economics , year =

    Gabaix, Xavier and Landier, Augustin , title =. The Quarterly Journal of Economics , year =

    work page

  31. [31]

    , title =

    Baker, George P. , title =. Journal of Political Economy , year =

    work page

  32. [32]

    Journal of Law, Economics, and Organization , year =

    Holmstrom, Bengt and Milgrom, Paul , title =. Journal of Law, Economics, and Organization , year =

    work page

  33. [33]

    and Xie, Jim , title =

    Feltham, Gerald A. and Xie, Jim , title =. The Accounting Review , year =

    work page

  34. [34]

    , title =

    Baker, George and Gibbons, Robert and Murphy, Kevin J. , title =. The Quarterly Journal of Economics , year =

    work page

  35. [35]

    American Economic Review , year =

    Mas, Alexandre and Moretti, Enrico , title =. American Economic Review , year =

    work page

  36. [36]

    Peer Effects in the Workplace , journal =

    Cornelissen, Thomas and Dustmann, Christian and Sch. Peer Effects in the Workplace , journal =. 2017 , volume =

    work page 2017

  37. [37]

    The Review of Economic Studies , year =

    Waldinger, Fabian , title =. The Review of Economic Studies , year =

    work page

  38. [38]

    and Wang, Jialan , title =

    Azoulay, Pierre and Graff Zivin, Joshua S. and Wang, Jialan , title =. The Quarterly Journal of Economics , year =

    work page

  39. [39]

    Peer Effects and Social Networks in Education , journal =

    Calv. Peer Effects and Social Networks in Education , journal =. 2009 , volume =

    work page 2009

  40. [40]

    and Rosen, Sherwin , title =

    Lazear, Edward P. and Rosen, Sherwin , title =. Journal of Political Economy , year =

    work page

  41. [41]

    American Economic Review , year =

    Moldovanu, Benny and Sela, Aner , title =. American Economic Review , year =

    work page

  42. [42]

    , title =

    Konrad, Kai A. , title =

    work page

  43. [43]

    2011 , volume =

    Tournaments Without Prizes: Evidence from Personnel Records , journal =. 2011 , volume =

    work page 2011

  44. [44]

    Journal of Public Economics , year =

    Azmat, Ghazala and Iriberri, Nagore , title =. Journal of Public Economics , year =

    work page

  45. [45]

    Journal of Economics & Management Strategy , year =

    Azmat, Ghazala and Iriberri, Nagore , title =. Journal of Economics & Management Strategy , year =

    work page

  46. [46]

    , title =

    Lazear, Edward P. , title =. American Economic Review , year =

    work page

  47. [47]

    The Quarterly Journal of Economics , year =

    Bandiera, Oriana and Barankay, Iwan and Rasul, Imran , title =. The Quarterly Journal of Economics , year =

    work page

  48. [48]

    Econometrica , year =

    Bandiera, Oriana and Barankay, Iwan and Rasul, Imran , title =. Econometrica , year =

    work page

  49. [49]

    Journal of the European Economic Association , year =

    Bandiera, Oriana and Barankay, Iwan and Rasul, Imran , title =. Journal of the European Economic Association , year =

    work page

  50. [50]

    Kelsey , title =

    Ashraf, Nava and Bandiera, Oriana and Jack, B. Kelsey , title =. Journal of Public Economics , year =

    work page

  51. [51]

    Talent Hoarding in Organizations

    Talent hoarding in organizations , author=. arXiv preprint arXiv:2206.15098 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

This paper was first reviewed by glm-5.2 on July 9, 2026.