  On-line firms deploy suites of software platforms, where each platform is
designed to interact with users during a certain activity, such as browsing,
chatting, socializing, emailing, driving, etc. The economic and incentive
structure of this exchange, as well as its algorithmic nature, have not been
explored to our knowledge. We model this interaction as a Stackelberg game
between a Designer and one or more Agents. We model an Agent as a Markov chain
whose states are activities; we assume that the Agent's utility is a linear
function of the steady-state distribution of this chain. The Designer may
design a platform for each of these activities/states; if a platform is adopted
by the Agent, the transition probabilities of the Markov chain are affected,
and so is the objective of the Agent. The Designer's utility is a linear
function of the steady state probabilities of the accessible states minus the
development cost of the platforms. The underlying optimization problem of the
Agent -- how to choose the states for which to adopt the platform -- is an MDP.
If this MDP has a simple yet plausible structure (the transition probabilities
from one state to another only depend on the target state and the recurrent
probability of the current state) the Agent's problem can be solved by a greedy
algorithm. The Designer's optimization problem (designing a custom suite for
the Agent so as to optimize, through the Agent's optimum reaction, the
Designer's revenue), is NP-hard to approximate within any finite ratio;
however, the special case, while still NP-hard, has an FPTAS. These results
generalize from a single Agent to a distribution of Agents with finite support,
as well as to the setting where the Designer must find the best response to the
existing strategies of other Designers. We discuss other implications of our
results and directions of future research.
