  We investigate the algorithmic problem of selling information to agents who
face a decision-making problem under uncertainty. We adopt the model recently
proposed by Bergemann et al. [BBS18], in which information is revealed through
signaling schemes called experiments. In the single-agent setting, any
mechanism can be represented as a menu of experiments. Our results show that
the computational complexity of designing the revenue-optimal menu depends
heavily on the way the model is specified. When all the parameters of the
problem are given explicitly, we provide a polynomial time algorithm that
computes the revenue-optimal menu. For cases where the model is specified with
a succinct implicit description, we show that the tractability of the problem
is tightly related to the efficient implementation of a Best Response Oracle:
when it can be implemented efficiently, we provide an additive FPTAS whose
running time is independent of the number of actions. On the other hand, we
provide a family of problems, where it is computationally intractable to
construct a best response oracle, and we show that it is NP-hard to get even a
constant fraction of the optimal revenue. Moreover, we investigate a
generalization of the original model by Bergemann et al. [BBS18] that allows
multiple agents to compete for useful information. We leverage techniques
developed in the study of auction design (see e.g. [CDW12a], [AFHHM12],
[CDW12b], [CDW13a], [CDW13b]) to design a polynomial time algorithm that
computes the revenue-optimal mechanism for selling information.
