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Abstract:
This paper endogenizes the (unweighted) network for the seminal model presented in Ballester et al. (2006) by way of a simple simultaneous move game. Agents choose to whom to connect and how much effort to exert. Effort levels display local strategiccomplementarities and global strategic substitutes. I show that all pairwise Nash equilibrium networks are nested split graphs. In these networks the ranking of agents based on Bonacich centrality (as well as inter-centrality) coincides with a much simplermeasure: degree centrality. As in Ballester et al. (2006), key player policies are studied, which aim at minimizing aggregate effort levels via the elimination of an agent from the network. However, in the spirit of network formation, the remaining agents in the network may now not only revise their effort decisions, but also adapt their linking behavior. I show that, if the parameter governing global strategic substitutes is sufficiently small, then eliminating an agent that is most central leads to a maximaldecrease in aggregate effort levels. This mirrors the results in Ballester et al. (2006). However, when global strategic substitutes are large, then, different from Ballester et al. (2006), eliminating an agent that is most central may not be optimal. These results are relevant for a wide range of applications, such as juvenile delinquency and crime, bank bailouts and R&D expenditure of firms.