  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.
