Unions and Key Players in Network Games with Conflicts and Spillovers

We study network games with social and private dissonance where each player in the network exerts some costly efforts. Players may belong to unions and members of each union choose their efforts by maximizing the joint utility of the union. Each player not only benefits from the aggregate effort and efforts of network neighbors are strategic complements, but also suffers disutility when her effort differs from her neighbors’ efforts or is inconsistent with her ideal effort. We characterize the unique Nash equilibrium of the network game with unions and we define a union intercentrality measure for finding the key player whose removal has the highest impact on the aggregate effort level. We explore the role of unions in fostering effort levels and we consider two alternative policies: the key addition to an existing union and the key union that generates the highest total effort. We investigate the stability of unions