基于马尔可夫链的Stackelberg博弈模型在网络教育论坛师生互动中的应用
Improving Teacher-Student Interactions in Online Educational Forums using a Markov Chain based Stackelberg Game Model
摘要：
随着互联网的迅速普及，教育领域在学生和教师如何在课堂上互动方面发生了巨大的变化。在线学习现在有不止一种形式，包括利用技术来加强面对面的课堂，结合面对面会议和在线工作的混合课堂，以及完全在线的课程。此外，在线课堂通常由在线教育论坛（OEF）组成，学生和教师在论坛上讨论开放式问题，以更好地了解主题。然而，经验研究一再表明，这些在线课程的辍学率非常高，部分原因是注册学生缺乏动力。我们在两个学期的研究生水平的课程与OEFs的学生行为进行实证比较。我们确定的关键参数，如有效的激励设计，学生的异质性，和超级海报现象的动态OEF。出于实证观察，我们提出了一个分析模型的基础上连续时间马尔可夫链（CTMCs）捕捉教师-学生的互动OEF。使用CTMC的集总性的概念，我们计算稳态和瞬态概率以及教师和学生的预期净回报。我们制定了一个混合整数线性规划，认为OEF作为一个单一的领导者，多个追随者Stackelberg游戏。通过模拟，我们观察到学生在参与中表现出不同程度的非单调性（随着教师参与度的增加）。我们还研究了教师偏见和预算对学生参与水平的影响。我们的模型展示了经验观察到的超级海报现象在某些参数配置下，并建议教师最大限度地提高学生参与开放式教学的最佳计划。
英文摘要：
With the rapid proliferation of the Internet, the area of education has undergone a massive transformation in terms of how students and instructors interact in a classroom. Online learning now takes more than one form, including the use of technology to enhance a face-to-face class, a hybrid class that combines both face-to-face meetings and online work, and fully online courses. Further, online classrooms are usually composed of an online education forum (OEF) where students and instructor discuss open-ended questions for gaining better understanding of the subject. However, empirical studies have repeatedly shown that the dropout rates in these online courses are very high partly due to the lack of motivation among the enrolled students. We undertake an empirical comparison of student behavior in OEFs associated with a graduate-level course during two terms. We identify key parameters dictating the dynamics of OEFs like effective incentive design, student heterogeneity, and super-posters phenomenon. Motivated by empirical observations, we propose an analytical model based on continuous time Markov chains (CTMCs) to capture instructor-student interactions in an OEF. Using concepts from lumpability of CTMCs, we compute steady state and transient probabilities along with expected net-rewards for the instructor and the students. We formulate a mixed-integer linear program which views an OEF as a single-leader-multiple-followers Stackelberg game. Through simulations, we observe that students exhibit varied degree of non-monotonicity in their participation (with increasing instructor involvement). We also study the effect of instructor bias and budget on the student participation levels. Our model exhibits the empirically observed super-poster phenomenon under certain parameter configurations and recommends an optimal plan to the instructor for maximizing student participation in OEFs.
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