Despite the conventional wisdom that proactive security is superior to reactive security, we show that reactive security can be competitive with proactive security as long as the reactive defender learns from past attacks instead of myopically overreacting to the last attack. Our game-theoretic model follows common practice in the security literature by making worst-case assumptions about the attacker: we grant the attacker complete knowledge of the defender’s strategy and do not require the attacker to act rationally. In this model, we bound the competitive ratio between a reactive defense algorithm (which is inspired by online learning theory) and the best fixed proactive defense. Additionally, we show that, unlike proactive defenses, this reactive strategy is robust to a lack of information about the attacker’s incentives and knowledge.
Four kinds of marginal returns to security investment to protect an information set are decrease, first increase and then decrease (logistic function), increase, and constancy. Gordon, L. A. and Loeb, M. (ACM Trans. Inf. Syst. Secur., 5:438---457, 2002). find for decreasing marginal returns that a firm invests maximum 37 (1? ?e) of the expected loss from a security breach, and that protecting moderately rather than extremely vulnerable information sets may be optimal. This article presents classes of all four kinds where the optimal investment is no longer capped at 1? ?e. First, investment in information security activities for the logistic function is zero for low vulnerabilities, jumps in a limited "bang-bang" manner to a positive level for intermediate vulnerabilities, and thereafter increases concavely in absolute terms. Second, we present an alternative class with decreasing marginal returns where the investment increases convexly in the vulnerability until a bound is reached, investing most heavily to protect the extremely vulnerable information sets. For the third and fourth kinds the optimal investment is of an all-out "bang-bang" nature, that is, zero for low vulnerabilities, and jumping to maximum investment for intermediate vulnerabilities. System reliability often depends on the effort of many individuals, making reliability a public good. It is well-known that purely voluntary provision of public goods may result in a free rider problem: individuals may tend to shirk, resulting in an inefficient level of the public good. How much effort each individual exerts will depend on his own benefits and costs, the efforts exerted by the other individuals, and the technology that relates individual effort to outcomes. In the context of system reliability, we can distinguish three prototype cases. This article presents an economic model that determines the optimal amount to invest to protect a given set of information. The model takes into account the vulnerability of the information to a security breach and the potential loss should such a breach occur. It is shown that for a given potential loss, a firm should not necessarily focus its investments on information sets with the highest vulnerability. Since extremely vulnerable information sets may be inordinately expensive to protect, a firm may be better off concentrating its efforts on information sets with midrange vulnerabilities. The analysis further suggests that to maximize the expected benefit from investment to protect information, a firm should spend only a small fraction of the expected loss due to a security breach. Despite general awareness of the importance of keeping one's system secure, and widespread availability of consumer security technologies, actual investment in security remains highly variable across the Internet population, allowing attacks such as distributed denial-of-service (DDoS) and spam distribution to continue unabated. By modeling security investment decision-making in established (e.g., weakest-link, best-shot) and novel games (e.g., weakest-target), and allowing expenditures in self-protection versus self-insurance technologies, we can examine how incentives may shift between investment in a public good (protection) and a private good (insurance), subject to factors such as network size, type of attack, loss probability, loss magnitude, and cost of technology. We can also characterize Nash equilibria and social optima for different classes of attacks and defenses. In the weakest-target game, an interesting result is that, for almost all parameter settings, more effort is exerted at Nash equilibrium than at the social optimum. We may attribute this to the "strategic uncertainty" of players seeking to self-protect at just slightly above the lowest protection level.