Adam Smith Business School

Professor Jérôme Renault, Toulouse School of Economics, University of Toulouse

"Strategic Experimentation with Privately Observed Payoffs", joint work in progress with Eilon Solan and Nicolas Vieille
Tuesday, 03 December 2024. 16:00-17:30
Room 141A, Adam Smith Business School

Abstract

We consider a strategic bandit problem with 2 states and 2 players having access to 2 identical arms: a safe arm with 0 cost and 0 return, and a risky arm delivering a positive payoff with positive probability only when the state is good. Each player observes the action, but not the payoff, of the other player, and no extra-communication is allowed. We show that at equilibrium there is always more experimentation than in the case of publicly observed payoffs, as players seeing the other player pulling the risky arm tend to believe that the state is good. A new cutoff $\hat{p}$ on the belief that the state is good, lower than the 1-player cutoff $p^*$, is introduced. At a pure sequential equilibria, in the bad state the last experimentation happens with a belief above $p^*$, and the final belief is below $\hat{p}$. There, the number of experiments is never too small but may be twice bigger than the socially optimal number. For mixed equilibria, in the bad state at least one final belief is below $\hat{p}$.

Bio

Jérôme Renault is a professor in the mathematics department of Toulouse School of Economics, a specialist in game theory and a member of the ANITI artificial intelligence institute. He previously worked at the Universities of Paris 1 and Paris-Dauphine, at the CNRS and at the Ecole Polytechnique.

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First published: 22 November 2024