Designing Frugal Best-Response Mechanisms for Social Network Coordination Games

Social coordination games have recently received a lot of attention since they model several kinds of interaction problems in social networks. However, the performance of these games at equilibrium may be very bad. This motivates the adoption of mechanisms for inducing a socially optimal state. In this work we consider the design of incentive-compatible best-response mechanisms (Nisan, Schapira, Valiant, Zohar, 2011) for social coordination games. Specifically, we would like to compute special fees that may be assigned to players in order to induce the optimum profile of a social coordination game. Moreover, we would like the mechanism to be frugal, that is it can be implemented without any cost. We show that a frugal incentive-compatible best-response mechanism for inducing the optimal profile of a two-strategy social coordination game always exists. Moreover, for such a mechanism, we investigate other properties inspired by envy-freeness, collusion-resistance and fairness. Finally, we show that extensions of the above results to other classes of games or to non-optimal profiles may be hard.