The Benefit of Sequentiality in Social Networks

This paper examines the benefit of sequentiality in the social networks. We adopt the elegant theoretical framework proposed by Ballester et al. (2006), wherein a fixed set of players non-cooperatively determine their contributions. This setting features payoff externalities and strategic complementarity amongst players. We first analyze the two-stage game in which players in the leader group make contributions prior to the follower group. Compared with the simultaneous-move benchmark, the equilibrium contribution by any individual player in any two-stage sequential-move game is unambiguously higher. We establish the isomorphism between the socially optimal selection of the leader and follower groups and the classical weighted maximum-cut problem. We give an exact index to characterize the key leader problem, and show that the key leader can be substantially different from the key player who impacts the networks most in the simultaneous-move game. We also provide some design principles for unweighted complete graphs and bipartite graphs. We then examine the structure of optimal mechanism and allow for arbitrary sequence of players' moves. We show that starting from any fixed sequence, the aggregate contribution always goes up while making simultaneous-moving players move sequentially. This suggests a robust rule of thumbs – any local modification towards the sequential-move game is beneficial. Pushing this idea to the extreme, the optimal sequence turns out to be a chain structure, i.e., players should move one by one. Our results continue to hold when either players exhibit strategic substitutes instead or the network designer's goal is to maximize the players' aggregate payoff rather than the aggregate contribution