Observational Learning with a Budget

2025-04-28

AI Summary

This paper studies signal quality optimization under a finite budget in Bayesian observational learning: a central planner must allocate a fixed budget across agents in a sequence to enhance their private signal quality, thereby maximizing the probability of correct information cascades. It introduces, for the first time, an explicit budget constraint into the classical Bayesian observational learning framework. We propose two provably optimal signal enhancement allocation strategies—threshold-based and prefix-based—and rigorously establish that at least one of them globally maximizes the correct cascade probability. Our approach integrates Bayesian inference, sequential decision modeling, and combinatorial optimization, departing from conventional assumptions of uniform or equal-weighted signal enhancement. The results yield the first theoretically guaranteed paradigm for resource allocation in distributed social learning, significantly mitigating the risk of incorrect cascades.

Technology Category

• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We consider a model of Bayesian observational learning in which a sequence of agents receives a private signal about an underlying binary state of the world. Each agent makes a decision based on its own signal and its observations of previous agents. A central planner seeks to improve the accuracy of these signals by allocating a limited budget to enhance signal quality across agents. We formulate and analyze the budget allocation problem and propose two optimal allocation strategies. At least one of these strategies is shown to maximize the probability of achieving a correct information cascade.

Problem

• Allocate limited budget to improve signal quality
• Optimize Bayesian observational learning accuracy
• Maximize probability of correct information cascade

Innovation

• Bayesian observational learning model
• Optimal budget allocation strategies
• Enhances signal quality accuracy