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Ambiguous Contracts

Paul Dütting, Michal Feldman, Daniel Peretz, Larry Samuelson

TL;DR

A model of ambiguous contracts is introduced, capturing many real-life scenarios where agents engage in contractual relations that leave some degree of uncertainty, where the celebrated hidden-action model and the classic notion of a contract are introduced.

Abstract

We explore the deliberate infusion of ambiguity into the design of contracts. We show that when the agent is ambiguity-averse and hence chooses an action that maximizes their minimum utility, the principal can strictly gain from using an ambiguous contract, and this gain can be arbitrarily high. We characterize the structure of optimal ambiguous contracts, showing that ambiguity drives optimal contracts towards simplicity. We also provide a characterization of ambiguity-proof classes of contracts, where the principal cannot gain by infusing ambiguity. Finally, we show that when the agent can engage in mixed actions, the advantages of ambiguous contracts disappear.

Ambiguous Contracts

TL;DR

A model of ambiguous contracts is introduced, capturing many real-life scenarios where agents engage in contractual relations that leave some degree of uncertainty, where the celebrated hidden-action model and the classic notion of a contract are introduced.

Abstract

We explore the deliberate infusion of ambiguity into the design of contracts. We show that when the agent is ambiguity-averse and hence chooses an action that maximizes their minimum utility, the principal can strictly gain from using an ambiguous contract, and this gain can be arbitrarily high. We characterize the structure of optimal ambiguous contracts, showing that ambiguity drives optimal contracts towards simplicity. We also provide a characterization of ambiguity-proof classes of contracts, where the principal cannot gain by infusing ambiguity. Finally, we show that when the agent can engage in mixed actions, the advantages of ambiguous contracts disappear.
Paper Structure (30 sections, 16 theorems, 82 equations, 9 figures, 3 tables)

This paper contains 30 sections, 16 theorems, 82 equations, 9 figures, 3 tables.

Table of Contents

  1. Introduction
  2. The Model
  3. Our Contribution
  4. Implications
  5. Related Literature
  6. The Model
  7. The Principal-Agent Model
  8. Classic Contracts
  9. Ambiguous Contracts
  10. Implementability
  11. Optimal Ambiguous Contracts
  12. The Advantage of Optimal Ambiguous Contracts
  13. The Structure of Optimal Ambiguous Contracts
  14. Optimal Monotone Ambiguous Contracts
  15. The Ambiguity Gap
  16. ...and 15 more sections

Key Result

Lemma 1

Suppose $\langle \tau, i \rangle$ is incentive compatible. Then there exists a consistent, incentive compatible ambiguous contract $\langle \tau', i \rangle$ from which the principal obtains expected payoff at least $\max_{t \in \tau} U_P({i} \mid {t})$.

Figures (9)

  • Figure 1: Instance $(c,r,p)$ for Example \ref{['mozart']}.
  • Figure 2: Instance $(c,r,p)$ for Example \ref{['ex:improve']}.
  • Figure 3: Instance $(c,r,p)$ for Example \ref{['ex:improve-mlrp']}.
  • Figure 4: Instance $(c,r,p)$ for Example \ref{['bach']}.
  • Figure 5: Instance $(c,r,p)$ for Example \ref{['hardy']}.
  • ...and 4 more figures

Theorems & Definitions (51)

  • Definition 1: Instance
  • Definition 2: MLRP
  • Definition 3
  • Definition 4: IC contract
  • Definition 5: IC ambiguous contract
  • Definition 6: Consistency
  • Lemma 1
  • proof
  • Proposition 1
  • Proposition 2
  • ...and 41 more