Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Allocating Resources under Strategic Misrepresentation

Yingkai Li, Xiaoyun Qiu

Abstract

We study how to allocate resources to participants who can strategically misrepresent their deservingness at a cost. A principal assigns item(s) (or money) among multiple agents on the basis of their costly signals. Each agent's signal reflects their private type in the absence of misrepresentation but can be inflated above their true type at a cost. The principal is a social planner who aims to maximize the weighted average of matching efficiency and a utilitarian objective. Strategic misrepresentation introduces novel incentive-compatibility constraints, under which we characterize the optimal mechanism. We apply our characterization to two kinds of markets, distinguished by resource scarcity, and show that the principal strictly benefits from randomizing the allocations based on costly signals when the population of participants is large enough. Interestingly, in large markets with scarce resources, the format of the optimal mechanism converges to a winner-takes-all contest; however, there is a non-diminishing value in randomizing allocations to middle types as the population of participants grows.

Allocating Resources under Strategic Misrepresentation

Abstract

We study how to allocate resources to participants who can strategically misrepresent their deservingness at a cost. A principal assigns item(s) (or money) among multiple agents on the basis of their costly signals. Each agent's signal reflects their private type in the absence of misrepresentation but can be inflated above their true type at a cost. The principal is a social planner who aims to maximize the weighted average of matching efficiency and a utilitarian objective. Strategic misrepresentation introduces novel incentive-compatibility constraints, under which we characterize the optimal mechanism. We apply our characterization to two kinds of markets, distinguished by resource scarcity, and show that the principal strictly benefits from randomizing the allocations based on costly signals when the population of participants is large enough. Interestingly, in large markets with scarce resources, the format of the optimal mechanism converges to a winner-takes-all contest; however, there is a non-diminishing value in randomizing allocations to middle types as the population of participants grows.
Paper Structure (26 sections, 18 theorems, 53 equations, 4 figures, 1 table)

This paper contains 26 sections, 18 theorems, 53 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Model
  4. Mechanisms.
  5. Interim approach.
  6. Symmetric environment.
  7. Optimal Mechanism
  8. Incentive compatibility
  9. Symmetric mechanism
  10. Optimal Contest
  11. Large Contests
  12. Scarce Resources
  13. Convex efficient allocation.
  14. Convergence results.
  15. Large-Scale Economy
  16. ...and 11 more sections

Key Result

Lemma 1

For any interim allocation--utility pair $(\boldsymbol{Q},\boldsymbol{U})$ that is implementable, there exists another interim allocation--utility pair $(\boldsymbol{Q}^\dagger,\boldsymbol{U}^\dagger)$ with monotone allocation $\boldsymbol{Q}^\dagger$ that is implementable and yields a weakly higher

Figures (4)

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

Theorems & Definitions (33)

  • Lemma 1: li2025mechanism
  • Lemma 2
  • Lemma 3
  • Theorem 1
  • Lemma 4
  • Proposition 1
  • Theorem 2: convergence of contest format
  • Theorem 3: non-convergence in payoffs
  • Theorem 4
  • Definition 1: feasibility
  • ...and 23 more