Learning Binary Multi-Scale Games on Networks

Network games are a natural modeling framework for strategic interactions of agents whose actions have local impact on others. Recently, a multi-scale network game model has been proposed to capture local effects at multiple network scales, such as among both individuals and groups. We propose a framework to learn the utility functions of binary multi-scale games from agents' behavioral data. Departing from much prior work in this area, we model agent behavior as following logit-response dynamics, rather than acting according to a Nash equilibrium. This defines a generative time-series model of joint behavior of both agents and groups, which enables us to naturally cast the learning problem as maximum likelihood estimation (MLE). We show that in the important special case of multi-scale linear-quadratic games, this MLE problem is convex. Extensive experiments using both synthetic and real data demonstrate that our proposed modeling and learning approach is effective in both game parameter estimation as well as prediction of future behavior, even when we learn the game from only a single behavior time series. Furthermore, we show how to use our framework to develop a statistical test for the existence of multi-scale structure in the game, and use it to demonstrate that real time-series data indeed exhibits such structure.