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Agent-Designed Contracts: How to Sell Hidden Actions

Martino Bernasconi, Matteo Castiglioni, Andrea Celli

TL;DR

This work proposes a model that enforces trust through economics incentives, and studies this delegation problem through the lens of contract design, with the overarching goal of enabling the computation of contracts that guarantee that the user can trust the service provider, even if their action is hidden.

Abstract

We study the problem faced by a service provider that has to sell services to a user. In our model the service provider proposes various payment options (a menu) to the user which may be based, for example, on the quality of the service. Then, the user chooses one of these options and pays an amount to the service provider, contingent on the observed final outcome. Users are not able to observe directly the action performed by the service provide to reach the final outcome. This might incentivize misconduct. Therefore, we propose a model that enforces trust through economics incentives. The problem has two crucial features: i) the service provider is responsible for both formulating the contract and performing the action for which the user issues payments, and ii) the user is unaware of the true action carried out by the service provider, which is hidden. We study this delegation problem through the lens of contract design, with the overarching goal of enabling the computation of contracts that guarantee that the user can trust the service provider, even if their action is hidden.

Agent-Designed Contracts: How to Sell Hidden Actions

TL;DR

This work proposes a model that enforces trust through economics incentives, and studies this delegation problem through the lens of contract design, with the overarching goal of enabling the computation of contracts that guarantee that the user can trust the service provider, even if their action is hidden.

Abstract

We study the problem faced by a service provider that has to sell services to a user. In our model the service provider proposes various payment options (a menu) to the user which may be based, for example, on the quality of the service. Then, the user chooses one of these options and pays an amount to the service provider, contingent on the observed final outcome. Users are not able to observe directly the action performed by the service provide to reach the final outcome. This might incentivize misconduct. Therefore, we propose a model that enforces trust through economics incentives. The problem has two crucial features: i) the service provider is responsible for both formulating the contract and performing the action for which the user issues payments, and ii) the user is unaware of the true action carried out by the service provider, which is hidden. We study this delegation problem through the lens of contract design, with the overarching goal of enabling the computation of contracts that guarantee that the user can trust the service provider, even if their action is hidden.
Paper Structure (21 sections, 44 theorems, 86 equations, 1 algorithm)

This paper contains 21 sections, 44 theorems, 86 equations, 1 algorithm.

Table of Contents

  1. Introduction
  2. Challenges, Results, and Techniques
  3. Related Work
  4. Model
  5. Model of interaction and optimization problem
  6. Optimization Problems under Deterministic Payment Schemes
  7. Computing the optimal direct menu is NP-Hard
  8. Computing optimal menus with small complexity
  9. The Unit-Demand Pricing Problem with Price-Floors
  10. Polynomial-Time Algorithm for Optimal Contracts with Small Menu Complexity
  11. Trade Off between Utility and Complexity of Menus
  12. Continuous actions and robustness
  13. Computing Robust Contracts
  14. Continuous Actions: Discretizing and Relaxing
  15. Menus of Randomized Payment Schemes
  16. ...and 6 more sections

Key Result

Theorem 1

For every constant $\rho>0$, there exists no polynomial-time algorithm that approximates up to within a $\rho$ multiplicative factor the value of the service provider's expected utility under an optimal (direct) menu of deterministic payment schemes, unless $\mathsf{P}=\mathsf{NP}$.

Theorems & Definitions (78)

  • Theorem 1
  • Definition 2: Feasible expected payments
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Corollary 1
  • Theorem 3
  • Theorem 4
  • Corollary 2
  • Lemma 4
  • ...and 68 more