Adaptive interventions for social welfare maximization in network games

We consider the problem of steering the actions of noncooperative players in quadratic network games to the social optimum. To this end, a central regulator modifies the marginal returns of the players, while the players' strategies are determined by continuous pseudo-gradient dynamics. Depending on the available information on the players parameters and network quantities, suitable static and dynamic intervention protocols are devised that maximize the social welfare at steady-state. We show that adaptive interventions can compensate for the lack of knowledge on network topology and coupling weights. Numerical examples are provided to demonstrate the effectiveness of the proposed interventions.