Human-computer Coalition Formation in Weighted Voting Games

Abstract

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.