Strategic Experimentation with Private Payoffs
Jérôme Renault, Eilon Solan, Nicolas Vieille
TL;DR
This paper extends strategic experimentation in exponential-bandit settings to environments with privately observed payoffs, revealing an encouragement mechanism that raises equilibrium exploration relative to public-outcome benchmarks. It develops a rigorous framework of Nash and sequential equilibria, introduces the encouragement cut-off hat p, and establishes that, in pure reasonable equilibria, the final amount of exploration is at least social optimal up to a small additive gap and at most a constant-factor above it. The analysis yields sharp bounds on over-experimentation and highlights the possibility of significant, yet bounded, over-experimentation under private payoffs; it also clarifies when pure reasonable SE exist or fail and why refinements are necessary. Collectively, the results provide foundational limits on information-driven experimentation and offer a detailed understanding of how private information reshapes strategic learning and welfare in dynamic environments.
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.