Network Formation under the Threat of Disruption

Abstract

The studies in this thesis are focused on the impact the presence of a network disruptor has on network formation models. In particular, we build two theoretical models to study the effect of network disruption on network formation and test the effect network disruption has on equilibrium selection in a laboratory experiment. We find that the network disruptor in each model we study has a significant effect on network formation and equilibrium selection. We first present a structural model of network design and disruption by modeling a two-stage full information game between a network designer and a network disruptor. We first investigate the threat of attack on the links of the network and then on the nodes of a network. Our results show that in a purely structural model between a network designer and a network disruptor the presence of a network disruptor leads to the network designer using additional links to build a robust network for relatively low linking costs and not connecting all nodes in one component for high linking costs. Thus, the network disruptor has a mostly negative effect, leading to over - or underconnectedness as compared to a benchmark case without a network disruptor. In the second part of this dissertation we then use the knowledge gained from this purely structural approach and look at the incentives of individual subjects in a network formation game, when the presence of a network disruptor is common knowledge. We introduce a network disruptor who can target the links of a network to a model of network formation in which the players are assumed to be rational, self-interested and myopic. In such a model in which the nodes themselves are individual players, the effect of a network disruptor is ambivalent. For low linking costs it leads to overconnectedness as compared to the benchmark case. However, for high linking costs it may lead to an increase in efficiency as connected networks are pairwise stable, while in the benchmark case only the empty network is pairwise stable. Finally in the network formation experiment, we find that overall groups almost exclusively reach an equilibrium network. They reach the empty network more often than the other two equilibria and also significantly more often when a network disruptor is present than when there is no disruptor. We test two competing hypotheses on the effect of a network disruptor on equilibrium selection, as his influence is either on the forwardlookingness of players or on their perceived risk. We find that the influence on the perceived risk is the dominant result. This implies that players will often end up in the empty network instead of a connected network. Overall the effect a network disruptor has on a network formation model thus depends on the model itself, as well as the costs of links and the possible equilibria. However, in all variants we have shown in this dissertation the presence of a network disruptor has a significant effect on the optimal network structure.