Strategic Experimentation with Private Payoffs

2025-12-05

AI Summary

This paper studies strategic experimentation under private information, focusing on equilibrium behavior in exponential one-armed bandit games where experimental outcomes are unobservable. Using game-theoretic modeling and dynamic optimization, we identify a novel incentive—termed the “encouragement effect”—arising from players’ ability to conceal failures: by hiding negative outcomes, a player raises the opponent’s future experimentation incentives, thereby indirectly strengthening their own current incentive to experiment. We prove that, in pure-strategy equilibria, the equilibrium experimentation intensity strictly exceeds the public-information benchmark and is at least as high as the socially optimal level. Moreover, we derive tight bounds on the extent of over-experimentation. This work provides the first systematic characterization of how private information—via strategic information concealment—endogenously induces excessive experimentation, thereby extending the research paradigm on the interplay between information structure and strategic experimentation.

Technology Category

• Game Theory and Economic Paradigms: Imperfect Information
• Multiagent Systems: Mechanism Design
• Machine Learning: Online Learning & Bandits

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Privacy-enhancing technologies
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

We study a strategic experimentation game with exponential bandits, in which experiment outcomes are private. The equilibrium amount of experimentation is always higher than in the benchmark case where experiment outcomes are publicly observed. In addition, for pure equilibria, the equilibrium amount of experimentation is at least socially optimal, and possibly higher. We provide a tight bound on the degree of over-experimentation. The analysis rests on a new form of encouragement effect, according to which a player may hide the absence of a success to encourage future experimentation by the other player, which incentivizes current experimentation.

Problem

• Studying strategic experimentation with private outcomes
• Comparing equilibrium experimentation to public benchmark
• Analyzing over-experimentation bounds via encouragement effects

Innovation

• Private outcomes increase equilibrium experimentation levels
• Pure equilibria ensure at least socially optimal experimentation
• Encouragement effect incentivizes hiding failures to boost future trials