Learning Quadratic Games on Networks
This work addresses the challenge of inferring hidden network structures in strategic interactions, which is incremental by extending existing analysis of known networks to learning from observable actions.
The paper tackles the problem of learning network games with linear-quadratic payoffs from observed individual actions when the underlying interaction network is hidden, proposing two novel frameworks that effectively recover the network structure and individual marginal benefits, as demonstrated in synthetic and real-world experiments.
Individuals, or organizations, cooperate with or compete against one another in a wide range of practical situations. Such strategic interactions are often modeled as games played on networks, where an individual's payoff depends not only on her action but also on that of her neighbors. The current literature has largely focused on analyzing the characteristics of network games in the scenario where the structure of the network, which is represented by a graph, is known beforehand. It is often the case, however, that the actions of the players are readily observable while the underlying interaction network remains hidden. In this paper, we propose two novel frameworks for learning, from the observations on individual actions, network games with linear-quadratic payoffs, and in particular, the structure of the interaction network. Our frameworks are based on the Nash equilibrium of such games and involve solving a joint optimization problem for the graph structure and the individual marginal benefits. Both synthetic and real-world experiments demonstrate the effectiveness of the proposed frameworks, which have theoretical as well as practical implications for understanding strategic interactions in a network environment.