Explainable Information Design

2025-08-19

AI Summary

This paper addresses the auditability and interpretability challenges posed by classical optimal signaling mechanisms in information design—such as randomization or disconnected partitions. We propose a class of interpretable, deterministic, monotonic *K*-partition signaling schemes: the continuous state space is partitioned into *K* ordered, connected intervals, and a unique signal is issued within each interval. We prove that, under this restriction, the worst-case approximation ratio is at most 2 (with a tight bound of 1/2). For Lipschitz utility functions, our method achieves a polynomial-time approximation; for piecewise-constant utilities, it attains 1/2-optimality. Our approach integrates monotonic partition construction, Lipschitz approximation, transformation from binary pooling to partitioning, and a tailored algorithm for piecewise-constant utilities. The resulting schemes significantly enhance interpretability, auditability, and communication efficiency of signals while preserving theoretical performance guarantees.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

The optimal signaling schemes in information design (Bayesian persuasion) problems often involve non-explainable randomization or disconnected partitions of state space, which are too intricate to be audited or communicated. We propose explainable information design in the context of information design with a continuous state space, restricting the information designer to use $K$-partitional signaling schemes defined by deterministic and monotone partitions of the state space, where a unique signal is sent for all states in each part. We first prove that the price of explainability (PoE) -- the ratio between the performances of the optimal explainable signaling scheme and unrestricted signaling scheme -- is exactly $1/2$ in the worst case, meaning that partitional signaling schemes are never worse than arbitrary signaling schemes by a factor of 2. We then study the complexity of computing optimal explainable signaling schemes. We show that the exact optimization problem is NP-hard in general. But for Lipschitz utility functions, an $varepsilon$-approximately optimal explainable signaling scheme can be computed in polynomial time. And for piecewise constant utility functions, we provide an efficient algorithm to find an explainable signaling scheme that provides a $1/2$ approximation to the optimal unrestricted signaling scheme, which matches the worst-case PoE bound. A technical tool we develop is a conversion from any optimal signaling scheme (which satisfies a bi-pooling property) to a partitional signaling scheme that achieves $1/2$ fraction of the expected utility of the former. We use this tool in the proofs of both our PoE result and algorithmic result.

Problem

• Optimizing explainable signaling schemes for continuous state space
• Analyzing the price of explainability in information design
• Developing efficient algorithms for approximately optimal partitions

Innovation

• Uses deterministic monotone partitions for explainable signaling
• Develops conversion from optimal to partitional schemes with 1/2 utility
• Provides polynomial-time algorithms for approximate optimal schemes