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Key Leaders in Social Networks

29 Pages Posted: 17 Feb 2013 Last revised: 29 Jun 2016

Junjie Zhou

National University of Singapore (NUS), Department of Economics

Ying-Ju Chen

School of Business and Management and School of Engineering

Date Written: January 5, 2015


This paper examines optimal targeting and sequencing strategies in the setup proposed by Ballester et al. (2006). The setup features payoff externalities and strategic complementarity among players, who non-cooperatively determine their contributions. We first analyze a two-stage game in which players in the leader group make contributions before the follower group. We construct an exact index to identify the (single) key leader, and demonstrate that the key leader can differ substantially from the key player who most influences the network in the simultaneous-move game. Using Taylor expansions on the strength of network effects, we establish an isomorphism between the optimal leader group selection (targeting) strategy and the classical weighted maximum-cut problem. This approach leads to some design principles for unweighted complete graphs and bipartite graphs.

We then allow for an arbitrary sequence of players' moves. If we refine any sequence by making some groups of simultaneous movers act in sequence, their aggregate contribution increases. Consequently, the optimal sequence is a chain structure. When players have homogeneous intrinsic valuations, any chain, arbitrarily ordered, maximizes the aggregate contribution. We further consider the possibility of shrinking the number of stages needed for the optimal sequence. In general, our results hold when the network game exhibits strategic substitutes.

Keywords: social network, dynamic games, key leader, sequencing, game theory

JEL Classification: D21, D29, D82

Suggested Citation

Zhou, Junjie and Chen, Ying-Ju, Key Leaders in Social Networks (January 5, 2015). Available at SSRN: or

Junjie Zhou (Contact Author)

National University of Singapore (NUS), Department of Economics ( email )



Ying-Ju Chen

School of Business and Management and School of Engineering ( email )

Clear Water Bay
Hong Kong

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