ICES: Small: Contribution Games in Social Networks

这个项目关注自利主体的网络形成。具体来说，它研究了社交网络中的贡献游戏，玩家/节点不仅与他人建立联系/关系，还决定了他们的联系强度。本项目将分析平衡解的质量，局部动力学的收敛性质，以及改善这些性质的机制。这项工作将产生有效的算法，用于计算贡献博弈的各种合理结果，以及通过给予玩家小激励来“推动”玩家形成更好结果的算法，使用近似算法来解决其他棘手的问题。更具体地说，本研究将考虑以下主题。(1)分析网络贡献游戏模型，该模型捕捉了玩家优化本地关系的本质。纳什均衡等概念对此类模型的用处有限，因此该项目转而关注两两均衡、强均衡和收敛动力学。(2)一般贡献游戏是网络贡献游戏的重要延伸：玩家为多人项目贡献，而不是成对关系。(3)中心性、友谊和利他主义。除了希望最大化所有项目/关系的总成功，玩家还可能希望建立联系，使自己在社交网络中处于有利位置，因此他们可能会尝试最大化“中心”概念，或者他们可能会关心整个网络的质量，就像在带有公共物品的游戏中一样。这个项目将分析玩家效用是这些考虑因素组合的游戏，并根据玩家效用函数的类型得出平衡解决方案的结构和质量的一般结果。社交网络渗透到人类生活的方方面面，影响着从流行病的传播到找工作的能力等方方面面。如今，社交网络上的数据变得更容易收集，了解社交网络形成的结构、属性和动机已成为一个重要的研究课题。通过明确地考虑社会网络中纽带的强度，而不仅仅是它们的存在，这项工作将为社会网络的博弈论模型增加一个新的维度，并获得对参与者行为和社会网络结构的新见解。这项研究或许还能提供一些有效的方法，通过给予社交网络参与者一些小的激励，来“推动”他们形成更好的结果。此外，该项目将为有限合谋系统的分析提供新的技术。在贡献游戏中，参与者除了关心自己的本地成功之外，还关心中心性、友谊和利他主义，这将是理解这种玩家激励组合下的社交网络结构的第一个主要尝试。该项目将包括与从事社会网络研究的理论和应用研究人员的合作，包括来自复杂系统、流行病学、社会学和管理学院的研究人员。由于对社交网络的广泛兴趣，这个项目可能会在上面提到的许多领域激发新的方法。最后，这项研究将得到PI的教育计划的大力支持，该计划包括教授几门带有研究成分的课程，组织一个关于这个主题的研讨会，并招募几名研究生和本科生参与这个项目。

This project focuses on network formation by self-interested agents. Specifically, it studies contribution games in social networks, where players/nodes not only form connections/relationships with others, but also determine the intensity of their connections. This project will analyze the quality of equilibrium solutions, convergence properties of local dynamics, and mechanisms to improve these properties. This work will result in efficient algorithms for computing various reasonable outcomes of contribution games, and algorithms for "nudging" the players to form better outcomes by giving them small incentives, using approximation algorithms for otherwise intractable problems. More concretely, this research will consider the following topics. (1) Analyzing a model of Network Contribution Games that captures the essence of players optimizing their local relationships. Concepts such as Nash equilibrium are of limited usefulness for such models, so the project instead focuses on pairwise equilibrium, strong equilibrium, and convergence dynamics. (2) General Contribution Games are an important extension of network contribution games: instead of pairwise relationships, players contribute to many-person projects. (3) Centrality, Friendship, and Altruism. Other than the desire to maximize total success of all projects/relationships players are involved in, they may also desire to form connections that make them well-positioned in the social network, and so attempt to maximize some notion of "centrality" or they may care about the quality of the network as a whole, as in games with public goods. This project will analyze games where the utility of a player is a combination of such considerations, and derive general results on the structure and quality of equilibrium solutions depending on the types of player utility functions.Social networks pervade most aspects of human life, and affect everything from the spread of epidemics to the ability to find a job. Now that data on social networks has become easier to collect, understanding the structure, properties, and incentives of social network formation has become a crucial research topic. By explicitly taking into account the strength of bonds in a social network, and not just their existence, this work will add a new dimension to game-theoretic models of social networks, and obtain new insight into participant behavior, and into the structure of social networks. This work may also suggest efficient methods for "nudging" the participants of a social network to form better outcomes by giving them small incentives. In addition, this project will contribute new techniques for analyzing systems with limited collusion. The study of contribution games where participants care about centrality, friendship, and altruism in addition to their local success, will be the first major attempt to understand the structure of social networks under such a combination of player incentives. This project will include collaborations with both theoretical and applied researchers working on social networks, including researchers from complex systems, epidemiology, sociology, and the school of management. Because of wide-spread interest in social networks, this project may inspire new approaches in many of the fields mentioned above. Finally, this research will be strongly complimented by the PI's education plan, which includes teaching several courses with research components, forming a workshop on this topic, and recruiting several graduate and undergraduate students to work on this project.