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Task assignment as dynamic incentives

Yonghang Ji, Allen Vong

TL;DR

The paper analyzes dynamic moral hazard in repeated, non-monetary task assignments where allocation is inseparable from production and rivalrous. It shows that the unique, uniformly efficient incentive provision takes the form of first-order rotation, a strict, evolving priority ranking that ensures effort incentives while preserving rivalrous constraints. This mechanism implies that, even among ex ante identical workers, continuation payoffs (and thus average workloads) become strictly ranked, revealing a pervasive efficiency-equality tension. The authors show structural organizational tools—larger workforces and higher monitoring precision—can expand the efficiency scope while reducing inequality, whereas payoff-based instruments raise inequality; maintaining uniform efficiency thus favors structural design. The results have practical implications for algorithmic management and regulatory debates on transparency, offering a nonmonetary justification for observed assignment-based inequalities and guidance on instrument choice to pursue efficiency without exacerbating disparities.

Abstract

We study repeated assignment of a task among workers as an incentive instrument for effort. Unlike traditional instruments, task assignment is inseparable from production and rivalrous: it both provides incentives and determines who produces, while necessarily excluding others. We show that workers are optimally assigned the task through a strict, evolving priority ranking. In every continuation, workers' expected average workloads differ, even when they are technologically independent and symmetric in all aspects. Consequently, our results highlight that the efficiency-equality tension is more pervasive than previously recognized. We further examine design instruments that expand the scope of efficiency without aggravating worker inequality.\bigskip

Task assignment as dynamic incentives

TL;DR

The paper analyzes dynamic moral hazard in repeated, non-monetary task assignments where allocation is inseparable from production and rivalrous. It shows that the unique, uniformly efficient incentive provision takes the form of first-order rotation, a strict, evolving priority ranking that ensures effort incentives while preserving rivalrous constraints. This mechanism implies that, even among ex ante identical workers, continuation payoffs (and thus average workloads) become strictly ranked, revealing a pervasive efficiency-equality tension. The authors show structural organizational tools—larger workforces and higher monitoring precision—can expand the efficiency scope while reducing inequality, whereas payoff-based instruments raise inequality; maintaining uniform efficiency thus favors structural design. The results have practical implications for algorithmic management and regulatory debates on transparency, offering a nonmonetary justification for observed assignment-based inequalities and guidance on instrument choice to pursue efficiency without exacerbating disparities.

Abstract

We study repeated assignment of a task among workers as an incentive instrument for effort. Unlike traditional instruments, task assignment is inseparable from production and rivalrous: it both provides incentives and determines who produces, while necessarily excluding others. We show that workers are optimally assigned the task through a strict, evolving priority ranking. In every continuation, workers' expected average workloads differ, even when they are technologically independent and symmetric in all aspects. Consequently, our results highlight that the efficiency-equality tension is more pervasive than previously recognized. We further examine design instruments that expand the scope of efficiency without aggravating worker inequality.\bigskip

Paper Structure

This paper contains 25 sections, 9 theorems, 36 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Related literature.
  3. Baseline model
  4. The structure of incentives
  5. Uniformly efficient assignment
  6. Efficiency and inequality
  7. Organizational design
  8. Extensions
  9. Commitment power.
  10. Idiosyncratic effort cost.
  11. Desirable task.
  12. Time-varying tasks.
  13. Multiple tasks.
  14. Limited worker information.
  15. Concluding comments
  16. ...and 10 more sections

Key Result

Lemma 1

In any efficient equilibrium, at any history $h_t$ on path where worker $i$ is assigned with positive probability, and

Figures (2)

  • Figure 1: First-order rotation with three workers
  • Figure 2: Symmetric treatment of unassigned workers

Theorems & Definitions (14)

  • Definition 1: Uniform efficiency
  • Lemma 1: Production-inseparable and rivalry-constrained incentives
  • Definition 2: First-order rotation
  • Theorem 1: Characterization
  • Proposition 1: Efficiency-equality tension
  • Proposition 2: Structural versus payoff instruments
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Lemma 5
  • ...and 4 more