论文标题
平台设计问题
The Platform Design Problem
论文作者
论文摘要
在线公司部署了软件平台的套件,每个平台都旨在在一定活动中与用户进行交互,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,尚未探索我们所知。我们将这种互动建模为设计师和一个或多个代理商之间的Stackelberg游戏。我们将代理人建模为马尔可夫链,其状态是活动;我们假设代理的效用是该链的稳态分布的线性函数。设计师可以为每个活动/州设计一个平台;如果代理采用平台,则会影响马尔可夫链的过渡概率,而代理的目的也是如此。设计师的实用程序是可访问状态的稳态概率的线性函数,减去平台的开发成本。代理的基本优化问题 - 如何选择采用平台的状态 - 是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过渡概率仅取决于目标状态,并且当前状态的反复概率)可以通过贪婪的算法来解决。设计师的优化问题(为代理设计定制套件,以通过代理的最佳反应(设计师的收入)优化NP在任何有限比率之内都可以近似;但是,特殊情况虽然仍然是NP-HARD,但仍有FPTA。这些结果从单个代理到具有有限支持的代理商的分布以及设计师必须找到对其他设计师现有策略的最佳响应的设置。我们讨论了我们的结果和未来研究方向的其他含义。
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.