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.
Keywords: strategic exploration, bandits, social learning, heterogenous priors
JEL Classification: D83
∗
I am thankful to Ian Ball, Stephen Morris, and Kartik Vira for detailed comments and feedback. I also
thank Anne Carlstein and Nathaniel Hickok for insightful suggestions.
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.
Keywords: strategic exploration, bandits, social learning, heterogenous priors
JEL Classification: D83
∗
I am thankful to Ian Ball, Stephen Morris, and Kartik Vira for detailed comments and feedback. I also
thank Anne Carlstein and Nathaniel Hickok for insightful suggestions.
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