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Dynamic Mechanism Design without Monetary Transfers: A Queueing Theory Approach

Zihao Li, Xuandong Chen

TL;DR

This paper addresses dynamic allocation of scarce resources without monetary transfers under stochastic arrivals. It develops a Markovian, steady-state framework in which the principal uses a Dynamic Threshold Mechanism with state-dependent admission and allocation cutoffs, coupled with costly verification, to optimally screen private types. The main contributions are the two-threshold policy, the NAD constraint, and a rigorous relaxation-and-verification approach that yields explicit comparative statics and large-market benchmarks. The findings have practical relevance for public programs and organizational capital budgeting, offering actionable guidance on how to modulate admission and allocation thresholds as arrivals, costs, or storage constraints change. Overall, the work provides a tractable, policy-relevant mechanism-design toolkit for intertemporal, transfer-free resource allocation in dynamic settings.

Abstract

We study the design of optimal allocation mechanisms in an environment where agents and goods arrive stochastically. Agents have private types that determine the principal payoff. Either agents or goods can be held in a queue at a flow cost until allocation. The principal cannot use monetary transfers, but can verify agents types at a cost. We characterize the optimal mechanism at the steady state of the system. It is a dynamic threshold mechanism in which the principal sets type thresholds for agent admission and goods allocation. These thresholds depend on the current state of the mechanism. The model applies to public programs such as public housing and grant allocation, and to allocation problems within organizations such as capital budgeting.

Dynamic Mechanism Design without Monetary Transfers: A Queueing Theory Approach

TL;DR

This paper addresses dynamic allocation of scarce resources without monetary transfers under stochastic arrivals. It develops a Markovian, steady-state framework in which the principal uses a Dynamic Threshold Mechanism with state-dependent admission and allocation cutoffs, coupled with costly verification, to optimally screen private types. The main contributions are the two-threshold policy, the NAD constraint, and a rigorous relaxation-and-verification approach that yields explicit comparative statics and large-market benchmarks. The findings have practical relevance for public programs and organizational capital budgeting, offering actionable guidance on how to modulate admission and allocation thresholds as arrivals, costs, or storage constraints change. Overall, the work provides a tractable, policy-relevant mechanism-design toolkit for intertemporal, transfer-free resource allocation in dynamic settings.

Abstract

We study the design of optimal allocation mechanisms in an environment where agents and goods arrive stochastically. Agents have private types that determine the principal payoff. Either agents or goods can be held in a queue at a flow cost until allocation. The principal cannot use monetary transfers, but can verify agents types at a cost. We characterize the optimal mechanism at the steady state of the system. It is a dynamic threshold mechanism in which the principal sets type thresholds for agent admission and goods allocation. These thresholds depend on the current state of the mechanism. The model applies to public programs such as public housing and grant allocation, and to allocation problems within organizations such as capital budgeting.
Paper Structure (64 sections, 8 theorems, 246 equations, 2 figures)

This paper contains 64 sections, 8 theorems, 246 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preview of Results.
  3. Contribution and Implication.
  4. Roadmap.
  5. Relation to Literature
  6. Mechanism Design with Costly Verification and without Transfers.
  7. Steady-state Mechanism Design.
  8. Dynamic Matching.
  9. Model
  10. Environment
  11. Preferences.
  12. Verification and Queue.
  13. Mechanism Space and Objective
  14. Steady State and Principal Payoff.
  15. Applications
  16. ...and 49 more sections

Key Result

Theorem 1

Under Assumptions ass:NAD and ass:static, the optimal mechanism exists and is a Dynamic Threshold Mechanism. In particular, the maximum agent queue length and goods queue length satisfy

Figures (2)

  • Figure : The default parameter values are $c_{w} = 0.281004$, $c_{v} = 0.073654$, $\mu = 0.764891$, and $\lambda = 1.610490$, and types are uniformly distributed on $[0,1]$. In the plots, there are ranges of parameter values for which $v_{2}^{*}$ does not appear. This reflects the fact that, in those regions, the principal optimally keeps at most one agent in the queue.
  • Figure : The default parameter values are $c_{v} = 0.12$, $c_{w} = 0.3$, $\lambda = 1.6$, $\mu = 1.1$, $c_{s} = 0.1$, $\underline{v} = -1$, and $\bar{v} = 3$, and types are uniformly distributed on $[-1,3]$. Dotted lines with square markers denote the cutoffs for the agent queue, whereas solid lines with dot markers denote the cutoffs for the inventory queue.

Theorems & Definitions (9)

  • Definition 1
  • Theorem 1
  • Theorem 2
  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Lemma 1: Uniform return probability
  • Lemma 2: Positive recurrence and unique stationary distribution
  • Proposition 4