Multiple Activities in Networks

Abstract

We consider a network model where individuals exert efforts in two types of activities that are interdependent. These activities can be either substitutes or complements. We provide a full characterization of the Nash equilibrium of this game for any network structure. We show, in particular, that quadratic games with linear best-reply functions aggregate nicely to multiple activities because equilibrium efforts obey similar formulas to that of the one-activity case. We then derive some comparative statics results showing how own productivity affects equilibrium efforts and how network density impacts equilibrium outcomes.

Keywords: Criminal networks, multiple activities, key player

JEL Classification: A14, D85, K42, Z13