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Multi-Agent Contract Design beyond Binary Actions

Federico Cacciamani, Martino Bernasconi, Matteo Castiglioni, Nicola Gatti

TL;DR

This work compares the two classes of mechanisms, designing a polynomial-time algorithm to compute almost optimal contracts and showing that randomized mechanisms provide an arbitrarily larger principal's utility than deterministic ones.

Abstract

We study hidden-action principal-agent problems with multiple agents. Unlike previous work, we consider a general setting in which each agent has an arbitrary number of actions, and the joint action induces outcomes according to an arbitrary distribution. We study two classes of mechanisms: a class of deterministic mechanisms that is the natural extension of single-agent contracts, in which the agents play a Nash equilibrium of the game induced by the contract, and a class of randomized mechanisms that is inspired by single-agent randomized contracts and correlated equilibria.

Multi-Agent Contract Design beyond Binary Actions

TL;DR

This work compares the two classes of mechanisms, designing a polynomial-time algorithm to compute almost optimal contracts and showing that randomized mechanisms provide an arbitrarily larger principal's utility than deterministic ones.

Abstract

We study hidden-action principal-agent problems with multiple agents. Unlike previous work, we consider a general setting in which each agent has an arbitrary number of actions, and the joint action induces outcomes according to an arbitrary distribution. We study two classes of mechanisms: a class of deterministic mechanisms that is the natural extension of single-agent contracts, in which the agents play a Nash equilibrium of the game induced by the contract, and a class of randomized mechanisms that is inspired by single-agent randomized contracts and correlated equilibria.
Paper Structure (43 sections, 40 theorems, 153 equations, 3 tables)

This paper contains 43 sections, 40 theorems, 153 equations, 3 tables.

Table of Contents

  1. Introduction
  2. Our Contributions
  3. Related Works
  4. Works on Single-Agent Contract Design
  5. Works on Multi-Agent Contract Design
  6. Preliminaries
  7. Contract Design
  8. Randomized contracts.
  9. Deterministic Contracts.
  10. Combinatorial Contracts and Virtual costs
  11. Combinatorial Contracts
  12. Virtual Cost Function
  13. The Power of Randomized Contracts
  14. Randomized Versus Deterministic Contracts
  15. Finding Approximately Optimal Randomized Contracts
  16. ...and 28 more sections

Key Result

Proposition 3.1

There exists an instance of the principal-multi-agent problem in which $\frac{\textsc{Opt}_\textsc{R}}{\textsc{Opt}_\textsc{D}} = \infty$.

Theorems & Definitions (63)

  • Remark 2.1
  • Proposition 3.1
  • Proposition 3.2
  • Remark 3.1
  • Lemma 3.1
  • Lemma 3.2
  • Theorem 3.1
  • Lemma 4.1
  • Theorem 4.1
  • Proposition 4.1
  • ...and 53 more