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 initiate their study in this paper. 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 (that is, the ones for which the platform has been adopted), minus the development cost of the platforms. The underlying optimization problem of the Agent -- that is, 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), while NP-hard, has an FPTAS. These results generalize, under mild additional assumptions, from a single Agent to a distribution of Agents with finite support. The Designer's optimization problem has abysmal "price of robustness", suggesting that learning the parameters of the problem is crucial for the Designer.

中文翻译：

---

平台设计问题

在线公司部署软件平台套件，其中每个平台旨在在特定活动中与用户交互，例如浏览、聊天、社交、发送电子邮件、驾驶等。 这种交换的经济和激励结构，以及据我们所知，其算法性质尚未被探索；我们在这篇论文中开始了他们的研究。我们将此交互建模为设计师和一个或多个代理之间的 Stackelberg 游戏。我们将代理建模为马尔可夫链，其状态是活动；我们假设代理的效用是该链稳态分布的线性函数。设计者可以为这些活动/状态中的每一个设计一个平台；如果Agent采用了一个平台，那么马尔可夫链的转移概率就会受到影响，Agent的目标也会受到影响。设计器的效用是可访问状态（即平台已被采用的状态）的稳态概率减去平台开发成本的线性函数。Agent 的底层优化问题——即如何选择采用平台的状态——是一个 MDP。如果这个 MDP 有一个简单而合理的结构（从一种状态到另一种状态的转换概率只取决于目标状态和当前状态的循环概率），Agent 的问题可以通过贪心算法来解决。Designer 的优化问题（为 Agent 设计定制套件，以便通过 Agent 的最佳反应优化 Designer 的收入），虽然 NP-hard，但有一个 FPTAS。这些结果概括，在温和的额外假设下，从单个代理到具有有限支持的代理分布。Designer 的优化问题具有极其糟糕的“稳健性代价”，这表明学习问题的参数对 Designer 至关重要。