  We consider how local and global decision policies interact in stopping time
problems such as quickest time change detection. Individual agents make myopic
local decisions via social learning, that is, each agent records a private
observation of a noisy underlying state process, selfishly optimizes its local
utility and then broadcasts its local decision. Given these local decisions,
how can a global decision maker achieve quickest time change detection when the
underlying state changes according to a phase-type distribution? The paper
presents four results. First, using Blackwell dominance of measures, it is
shown that the optimal cost incurred in social learning based quickest
detection is always larger than that of classical quickest detection. Second,
it is shown that in general the optimal decision policy for social learning
based quickest detection is characterized by multiple thresholds within the
space of Bayesian distributions. Third, using lattice programming and
stochastic dominance, sufficient conditions are given for the optimal decision
policy to consist of a single linear hyperplane, or, more generally, a
threshold curve. Estimation of the optimal linear approximation to this
threshold curve is formulated as a simulation-based stochastic optimization
problem. Finally, the paper shows that in multi-agent sensor management with
quickest detection, where each agent views the world according to its prior,
the optimal policy has a similar structure to social learning.
