平台设计问题
The Platform Design Problem
摘要：
在线公司部署软件平台套件，其中每个平台都被设计为在特定活动期间与用户交互，例如浏览，聊天，社交，电子邮件，驾驶等，这种交换的经济和激励结构以及其算法性质尚未被探索。我们将这种交互建模为设计师和一个或多个代理之间的Stackelberg游戏。我们的代理模型作为一个马尔可夫链的状态是活动，我们假设代理的效用是这个链的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平台;如果代理采用平台，则马尔可夫链的转移概率会受到影响，因此代理的目标也会受到影响。设计者的效用是可访问状态的稳定状态概率减去平台的开发成本的线性函数。Agent的底层优化问题--如何选择采用平台的状态--是一个MDP。如果该MDP具有简单但合理的结构（从一个状态到另一个状态的转移概率仅取决于目标状态和当前状态的复发概率），则Agent的问题可以通过贪心算法来解决。设计者的优化问题（设计一个自定义套件的代理，以便优化，通过代理的最佳反应，设计者的收入），是NP难近似在任何有限的比率;然而，特殊的情况下，虽然仍然NP难，有一个FPTAS。这些结果概括了从一个单一的代理代理的分布有限的支持，以及设置设计师必须找到最佳的反应，其他设计师的现有策略。我们讨论了我们的研究结果和未来的研究方向的其他影响。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
