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Screening Signal-Manipulating Agents via Contests

Yingkai Li, Xiaoyun Qiu

TL;DR

This paper analyzes screening under manipulation where signals reflect hidden, unproductive effort and resources are limited. It proves that welfare-maximizing mechanisms are contests and provides a detailed characterization of the optimal contest, showing that winner-takes-all is not generally optimal, especially with many agents or when items scale with agents. By deploying an interim allocation framework and incentive-compatibility analysis, the authors show that contests prevent information leakage and double-deviation, enabling efficient allocation with minimized effort. The study also explores large-number and large-scale settings, revealing that optimal contests exhibit simple, interpretable structures such as coarse ranking and randomization near critical types, with implications for policy design and real-world contests.

Abstract

We study the design of screening mechanisms subject to competition and manipulation. A social planner has limited resources to allocate to multiple agents using only signals manipulable through unproductive effort. We show that the welfare-maximizing mechanism takes the form of a contest and characterize the optimal contest. We apply our results to two settings: either the planner has one item or a number of items proportional to the number of agents. We show that in both settings, with sufficiently many agents, a winner-takes-all contest is never optimal. In particular, the planner always benefits from randomizing the allocation to some agents.

Screening Signal-Manipulating Agents via Contests

TL;DR

This paper analyzes screening under manipulation where signals reflect hidden, unproductive effort and resources are limited. It proves that welfare-maximizing mechanisms are contests and provides a detailed characterization of the optimal contest, showing that winner-takes-all is not generally optimal, especially with many agents or when items scale with agents. By deploying an interim allocation framework and incentive-compatibility analysis, the authors show that contests prevent information leakage and double-deviation, enabling efficient allocation with minimized effort. The study also explores large-number and large-scale settings, revealing that optimal contests exhibit simple, interpretable structures such as coarse ranking and randomization near critical types, with implications for policy design and real-world contests.

Abstract

We study the design of screening mechanisms subject to competition and manipulation. A social planner has limited resources to allocate to multiple agents using only signals manipulable through unproductive effort. We show that the welfare-maximizing mechanism takes the form of a contest and characterize the optimal contest. We apply our results to two settings: either the planner has one item or a number of items proportional to the number of agents. We show that in both settings, with sufficiently many agents, a winner-takes-all contest is never optimal. In particular, the planner always benefits from randomizing the allocation to some agents.
Paper Structure (41 sections, 26 theorems, 70 equations, 5 figures, 1 table)

This paper contains 41 sections, 26 theorems, 70 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. An Example
  4. Model
  5. Payoffs.
  6. General mechanism design.
  7. Contest design.
  8. Interim approach.
  9. Optimality of Contests
  10. Incentive compatibility.
  11. Payoff equivalence.
  12. Optimality of contests.
  13. Step 2: Showing that $U_i(\theta_i)\leq Q^\dagger_i(\theta_i)$ for all types $\theta_i$.
  14. Step 3: Optimality of contests.
  15. Strict suboptimality of VCG-format mechanism.
  16. ...and 26 more sections

Key Result

Lemma 1

An interim allocation--utility pair $(\boldsymbol{Q},\boldsymbol{U})$ with monotone $\boldsymbol{Q}$ is implementable by a contest if and only if $\boldsymbol{Q}$ is interim feasible, and for any agent $i$ with type $\theta_i$,The function $U_i$ may not be differentiable everywhere. For any type $\t

Figures (5)

  • Figure 1: Illustration of \ref{['cor:payoff equiv']}
  • Figure 2: Intuition for \ref{['thm:monotone optimal general']}
  • Figure 3: Optimal interim allocation rule under convex $Q_{\rm E}(\theta)$
  • Figure 4: Implementation of the optimal allocation rule
  • Figure 5: Optimal allocation and utility for large-scale economy in the limit

Theorems & Definitions (60)

  • Example 1: second-price-format mechanism
  • Example 2: contest
  • Definition 1
  • Definition 2
  • Lemma 1
  • Lemma 2
  • Proposition 1
  • Lemma 3
  • proof
  • Theorem 1: optimality of contests
  • ...and 50 more