This article proposes a negotiation game, based on the weighted voting paradigm in cooperative game theory, where agents need to form coalitions and agree on how to share the gains. Despite the prevalence of weighted voting in the real world, there has been little work studying people’s behavior in such settings. This work addresses this gap by combining game-theoretic solution concepts with machine learning models for predicting human behavior in such domains. We present a five-player online version of a weighted voting game in which people negotiate to create coalitions. We provide an equilibrium analysis of this game and collect hundreds of instances of people’s play in the game. We show that a machine learning model with features based on solution concepts from cooperative game theory (in particular, an extension of the Deegan-Packel Index) provide a good prediction of people’s decisions to join coalitions in the game. We designed an agent that uses the prediction model to make offers to people in this game and was able to outperform other people in an extensive empirical study. These results demonstrate the benefit of incorporating concepts from cooperative game theory in the design of agents that interact with people in group decision-making settings.

中文翻译：

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加权投票博弈中的人机联盟形成

本文提出了一种谈判博弈，基于合作博弈论中的加权投票范式，代理人需要形成联盟并就如何分享收益达成一致。尽管在现实世界中普遍存在加权投票，但研究人们在这种环境中的行为的工作却很少。这项工作通过将博弈论解决方案概念与机器学习模型相结合来预测这些领域中的人类行为，从而解决了这一差距。我们展示了一个五人在线版本的加权投票游戏，人们在其中协商建立联盟。我们提供了这个游戏的均衡分析，并收集了数百个人们在游戏中玩的实例。我们展示了一个机器学习模型，其特征基于合作博弈论的解决方案概念（特别是，Deegan-Packel 指数的扩展）可以很好地预测人们在游戏中加入联盟的决定。我们设计了一个代理，它使用预测模型向游戏中的人提供报价，并且能够在广泛的实证研究中胜过其他人。这些结果证明了在设计与群体决策环境中的人交互的代理时，将合作博弈论中的概念结合起来的好处。