Ambiguous Contracts (2302.07621v5)

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.

• The paper demonstrates that deliberately introduced ambiguity enables principals to extract higher utility in hidden-action contracts by leveraging agents’ worst-case evaluations.
• It establishes near-tight bounds on utility gains, showing that the ambiguity gap can reach up to n-1 compared to traditional contracts.
• Optimal ambiguous contracts can be simplified into finite single-outcome payments, and efficient algorithms are provided for their practical computation.

Ambiguous Contracts: A Theoretical Exploration

The paper "Ambiguous Contracts," authored by Paul Dütting, Michal Feldman, Daniel Peretz, and Larry Samuelson, contributes to contract theory by investigating the deliberate introduction of ambiguity into contract design. This exploration is driven by the observation that ambiguity is often inherent in real-world contracts, and the authors seek to model and analyze its potential advantages within a principal-agent framework.

Key Contributions and Results

The primary contribution of this paper is the analytical and computational exploration of optimal ambiguous contracts within a hidden-action principal-agent model. The authors specifically examine scenarios where an agent is ambiguity-averse and aims to maximize their minimum utility across possible contract outcomes.

Ambiguity Advantage and Optimal Contracts:

• Theoretical Insights: The authors demonstrate that ambiguity can enhance the principal's ability to extract utility from contracts by leveraging the agent's aversion to ambiguous outcomes. In scenarios where agents respond to the worst-case perception of ambiguity, principals can utilize ambiguous contracts to their advantage.
• Numerical Results: The paper establishes near-tight bounds on the potential increase in utility from ambiguous contracts. The ambiguity gap, defined as the ratio between the maximum utility with ambiguous contracts versus traditional contracts, can be as large as $n-1$, where $n$ represents the number of actions available to the agent.

Structural Properties:

• The paper reveals that optimal ambiguous contracts can be simplified to a finite set of single-outcome payment (SOP) contracts. The optimal number of these contracts is bounded by $\min\{m, n-1\}$, with $m$ being the number of outcomes.
• Under the Monotone Likelihood Ratio Property (MLRP), the analysis shows that optimal ambiguous contracts consist of at most two SOP contracts, showcasing an even greater level of simplification.

Algorithmic Implications:

• Efficient algorithms are put forth to compute optimal ambiguous contracts, leveraging the structural properties of these contracts. The computational complexity is $O(n^2 m)$ and improves to $O(n^2 + m)$ under MLRP, allowing for practical application in diverse scenarios.

Further Analysis:

• The authors identify "ambiguity-proof" classes of contracts, which cannot be improved upon using ambiguity. Through a clean geometric criterion termed "no proper crossing" (NPC), they characterize these classes. Notably, linear contracts fall into this category, offering an explanation for their widespread popularity due to inherent robustness against ambiguous enhancements.

Implications and Future Directions

The paper's findings suggest that ambiguity, while traditionally viewed as a hindrance, can be strategically employed to enhance contractual outcomes. This reframing has theoretical implications for extensions of contract theory where ambiguity is deliberately utilized as a tool for contract optimization.

Practical Implications:

• The results underscore the importance of acknowledging and potentially leveraging ambiguity in contract design, particularly in sectors where precise outcomes are challenging to define or observe, such as academia or creative industries.

Theoretical and Methodological Directions:

• Future research could expand on the behavioral assumptions regarding ambiguity aversion and max-min utility. Empirical validation of these assumptions in various real-world settings could further elucidate the practical applicability and modify the theoretical model to align more closely with observed behaviors.

Relation to Broader Economic Phenomena:

• The exploration of ambiguous contracts aligns with behavioral economic observations, such as the Ellsberg Paradox, and discussions surrounding ambiguity aversion's effects on decision making. By grounding their model within these theories, the authors contribute a nuanced perspective on how ambiguity can be systematically exploited, challenging traditional assumptions in economic theory.

In synthesis, the paper "Ambiguous Contracts" offers valuable insights into the intricacies of contract theory by introducing and rigorously analyzing the role of ambiguity. The findings not only provide a theoretical framework for understanding ambiguous contracts but also propose practical methodologies for deciding their optimal structure, laying the groundwork for potential empirical exploration and real-world application.