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Beliefs in Decision-Making Cascades
This work explores a social learning problem with agents having nonidentical
noise variances and mismatched beliefs. We consider an -agent binary
hypothesis test in which each agent sequentially makes a decision based not
only on a private observation, but also on preceding agents' decisions. In
addition, the agents have their own beliefs instead of the true prior, and have
nonidentical noise variances in the private signal. We focus on the Bayes risk
of the last agent, where preceding agents are selfish.
We first derive the optimal decision rule by recursive belief update and
conclude, counterintuitively, that beliefs deviating from the true prior could
be optimal in this setting. The effect of nonidentical noise levels in the
two-agent case is also considered and analytical properties of the optimal
belief curves are given. Next, we consider a predecessor selection problem
wherein the subsequent agent of a certain belief chooses a predecessor from a
set of candidates with varying beliefs. We characterize the decision region for
choosing such a predecessor and argue that a subsequent agent with beliefs
varying from the true prior often ends up selecting a suboptimal predecessor,
indicating the need for a social planner. Lastly, we discuss an augmented
intelligence design problem that uses a model of human behavior from cumulative
prospect theory and investigate its near-optimality and suboptimality.Comment: final version, to appear in IEEE Transactions on Signal Processin
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