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 Agents 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 Designers 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 Agents problem can be solved by a greedy algorithm. The Designers optimization problem (designing a custom suite for the Agent so as to optimize, through the Agents optimum reaction, the Designers 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.
Download