  We consider the problem of a decision-maker searching for information on
multiple alternatives when information is learned on all alternatives
simultaneously. The decision-maker has a running cost of searching for
information, and has to decide when to stop searching for information and
choose one alternative. The expected payoff of each alternative evolves as a
diffusion process when information is being learned. We present necessary and
sufficient conditions for the solution, establishing existence and uniqueness.
We show that the optimal boundary where search is stopped (free boundary) is
star-shaped, and present an asymptotic characterization of the value function
and the free boundary. We show properties of how the distance between the free
boundary and the diagonal varies with the number of alternatives, and how the
free boundary under parallel search relates to the one under sequential search,
with and without economies of scale on the search costs.
