Information aggregation in the public-payoff Markov equilibrium

Determine whether, in the version of the exponential bandit voting model with publicly observed payoff streams (under the same collective threshold rule for implementing the risky action), the unique Markov equilibrium in undominated strategies aggregates information as the number of agents N grows large; specifically, ascertain whether along the sequence of these equilibria the risky action is implemented in state H and the safe action in state L after some time with probability approaching one.

Background

The paper analyzes a dynamic collective experimentation model with privately observed payoffs and correlated types, characterizing a unique symmetric equilibrium and its large-population properties. It establishes conditions under which information is aggregated when payoffs are private and the collective decision follows a threshold rule.

In the concluding remarks, the author discusses the variant with publicly observed payoffs. While a unique Markov equilibrium in undominated strategies can be established (via extension of Strulovici, 2010), the paper explicitly states that it remains unresolved whether information is aggregated along the sequence of those equilibria as the number of agents grows large, due to the presence of numerous cut-offs without closed-form characterization. The only partial result noted is that in state L, when the population is large, the safe action is implemented almost immediately.