Network security and contagion

Azarakhsh Malekian
University of Toronto

In this work, we develop a theoretical model of security investments in a network of interconnected agents. The network connections introduce the possibility of cascading failures depending on either exogenous or endogenous attacks, as well as the profile of security investments of the agents. The general presumption in the literature, based on intuitive arguments or analysis of symmetric networks, is that because security investments create positive externalities on other agents, there will be underinvestment in security. We show that this reasoning is incomplete because of a first-order economic force: security investments are also strategic substitutes. In a general network (not necessarily symmetric), this implies that underinvestment by some agents will encourage overinvestment by others. We show that not only there will be overinvestment by some agents but also aggregate probabilities of infection in equilibrium can be lower than in the social optimum. We then provide sufficient conditions for underinvestment.
We also provide a tight characterization of equilibrium and socially optimal investment levels under sufficiently large investment cost assumption. The characterization is in terms of network topology, in which two new notions of network centrality, which we refer to as “blockedness centrality” and “bottleneck centrality”, emerges as the key notions and we explain the differences between these notions and the centrality measures used in the literature.
Finally, we show that when the attack location is endogenized (by assuming that the attacker chooses a probability distribution over the location of the attack in order to maximize damage), overinvestment occurs because of another reason, which is, greater investment by an agent shifts the attack location toward other parts of the network.
This is joint work with Prof. Daron Acemoglu and Prof. Asuman Ozdaglar.

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