Sequential Competition and the Strategic Origins of Preferential Attachment

Abstract

There exists a wide gap between the predictions of strategic models of network formation and empirical observations of the characteristics of socio-economic networks. Empirical observations underline a complex structure characterized by fat-tailed degree distribution, short average distance, large clustering coefficient and positive assortativity. Game theoretic models offer a detailed representation of individuals’ incentives but they predict the emergence of much simpler structures than these observed empirically. Random network formation processes, such as preferential attachment, provide a much better fit to empirical observations but generally lack micro-foundations. In order to bridge this gap, we propose to model network formation as extensive games and investigate under which conditions equilibria of these games are observationally equivalent with random network formation process. In particular, we introduce a class of games in which players compete with their predecessors and their successors for the utility induced by the links they form with other nodes in the network. Such sequential competition games can represent a number of strategic economic interactions such as oligopolistic competition in supply networks or diffusion of influence in opinion networks. We show that the focal equilibrium that emerges in this setting is one where players use probability distributions with full support and target the whole network with probabilities inversely proportional, to the utility of each node. Notably, when the utility of a node is inversely proportional to its degree, equilibrium play induces a preferential attachment process.