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Prior-free Collusion-proof Dynamic Mechanisms

Endre Csóka

TL;DR

The paper generalizes prior collusion-resistant dynamic mechanisms by introducing prior-free versions of the Guaranteed Utility Mechanism, applicable to both transferable and non-transferable utility settings. It develops a formal dynamic model with revelation and timing, defines universal feasibility and guaranteed utilities, and shows how to implement target welfare guarantees without fixed priors, using transfers or transfer-free schemes. A key result is a 1.283-approximation to Pareto efficiency in a repeated single-good allocation and a sequential good allocation construction that attains universal feasibility in TU, with NTU extensions and related robustness properties. The work advances robust mechanism design for dynamic multi-player environments and provides a framework for analyzing efficiency-robustness trade-offs under relaxed priors, with open questions about tightening bounds and extending to broader settings.

Abstract

For a general class of dynamic stochastic multi-player problems, Csóka, Liu, Rodivilov, and Teytelboym (2024) proposed prior-dependent mechanisms. The Guaranteed Utility Mechanism with transfers (TU-GUM) implements efficiency in a Guaranteed Utility Equilibrium (GUE). Its transfer-free variant (NTU-GUM) implements approximate efficiency in ε-GUE. In this paper, we define prior-free versions of both TU-GUM and NTU-GUM. As a special case, we believe that the new prior-free NTU-GUM implements a 1.283-approximation to Pareto efficiency for the repeated single good allocation problem in Fikioris, Banerjee, and Tardos (2024).

Prior-free Collusion-proof Dynamic Mechanisms

TL;DR

The paper generalizes prior collusion-resistant dynamic mechanisms by introducing prior-free versions of the Guaranteed Utility Mechanism, applicable to both transferable and non-transferable utility settings. It develops a formal dynamic model with revelation and timing, defines universal feasibility and guaranteed utilities, and shows how to implement target welfare guarantees without fixed priors, using transfers or transfer-free schemes. A key result is a 1.283-approximation to Pareto efficiency in a repeated single-good allocation and a sequential good allocation construction that attains universal feasibility in TU, with NTU extensions and related robustness properties. The work advances robust mechanism design for dynamic multi-player environments and provides a framework for analyzing efficiency-robustness trade-offs under relaxed priors, with open questions about tightening bounds and extending to broader settings.

Abstract

For a general class of dynamic stochastic multi-player problems, Csóka, Liu, Rodivilov, and Teytelboym (2024) proposed prior-dependent mechanisms. The Guaranteed Utility Mechanism with transfers (TU-GUM) implements efficiency in a Guaranteed Utility Equilibrium (GUE). Its transfer-free variant (NTU-GUM) implements approximate efficiency in ε-GUE. In this paper, we define prior-free versions of both TU-GUM and NTU-GUM. As a special case, we believe that the new prior-free NTU-GUM implements a 1.283-approximation to Pareto efficiency for the repeated single good allocation problem in Fikioris, Banerjee, and Tardos (2024).

Paper Structure

This paper contains 13 sections, 7 theorems, 35 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Example: allocation problem
  3. Transfer-free mechanism for a repeated game
  4. The general setup
  5. Utilities.
  6. Timing with the revelation mechanism.
  7. Strategies.
  8. Exiting and re-entering.
  9. Prior-free transferable utility mechanisms
  10. Sequential good allocation game
  11. Prior-free non-transferable utility mechanisms
  12. Open questions
  13. Acknowledgement

Key Result

Theorem 4.3

For each initial type vector and efficient decision policy $\chi$, the Guaranteed Utility Mechanism (GUM) implements in guaranteed utilities the same efficient utility profile as indicated by $\chi$.

Figures (1)

  • Figure 1: Numerical solution of \ref{['eq:ODE']} with $\lambda=1.28281$.

Theorems & Definitions (22)

  • Definition 4.1
  • Definition 4.2
  • Theorem 4.3: CLRT
  • Theorem 4.4
  • proof
  • Example 4.5
  • Lemma 4.6
  • proof
  • Theorem 4.7
  • proof
  • ...and 12 more