  We consider a monopoly information holder selling information to a
budget-constrained decision maker, who may benefit from the seller's
information. The decision maker has a utility function that depends on his
action and an uncertain state of the world. The seller and the buyer each
observe a private signal regarding the state of the world, which may be
correlated with each other. The seller's goal is to sell her private
information to the buyer and extract maximum possible revenue, subject to the
buyer's budget constraints. We consider three different settings with
increasing generality, i.e., the seller's signal and the buyer's signal can be
independent, correlated, or follow a general distribution accessed through a
black-box sampling oracle. For each setting, we design information selling
mechanisms which are both optimal and simple in the sense that they can be
naturally interpreted, have succinct representations, and can be efficiently
computed. Notably, though the optimal mechanism exhibits slightly increasing
complexity as the setting becomes more general, all our mechanisms share the
same format of acting as a consultant who recommends the best action to the
buyer but uses different and carefully designed payment rules for different
settings. Each of our optimal mechanisms can be easily computed by solving a
single polynomial-size linear program. This significantly simplifies
exponential-size LPs solved by the Ellipsoid method in the previous work, which
computes the optimal mechanisms in the same setting but without budget limit.
Such simplification is enabled by our new characterizations of the optimal
mechanism in the (more realistic) budget-constrained setting.
