Social learning via actions in bandit environments

TL;DR

This paper analyzes strategic exploration in Bayesian bandit environments with multiple agents, focusing on cascade equilibria where agents switch actions based on their beliefs, and explores implications for market behavior and contracting.

Contribution

It introduces the concept of cascade equilibria in multi-agent Bayesian bandit settings and examines their properties and implications for exploration and market dynamics.

Findings

Existence of cascade equilibria under certain conditions

Agents' exploration levels depend on initial priors

Most optimistic agent underexplores and can buy out others

Abstract

I study a game of strategic exploration with private payoffs and public actions in a Bayesian bandit setting. In particular, I look at cascade equilibria, in which agents switch over time from the risky action to the riskless action only when they become sufficiently pessimistic. I show that these equilibria exist under some conditions and establish their salient properties. Individual exploration in these equilibria can be more or less than the single-agent level depending on whether the agents start out with a common prior or not, but the most optimistic agent always underexplores. I also show that allowing the agents to write enforceable ex-ante contracts will lead to the most ex-ante optimistic agent to buy all payoff streams, providing an explanation to the buying out of smaller start-ups by more established firms.