A Strategic Analysis of Information Sharing Among Cyber Attackers

Abstract

We build a game theory model where the market design is such that one firm invests in security to defend against cyber attacks by two hackers. The firm has an asset, which is allocated between the three market participants dependent on their contest success. Each hacker chooses an optimal attack, and they share information with each other about the firm’s vulnerabilities. Each hacker prefers to receive information, but delivering information gives competitive advantage to the other hacker. We find that each hacker’s attack and information sharing are strategic complements while one hacker’s attack and the other hacker’s information sharing are strategic substitutes. As the firm’s unit defense cost increases, the attack is inverse U-shaped and reaches zero, while the firm’s defense and profit decrease, and the hackers’ information sharing and profit increase. The firm’s profit increases in the hackers’ unit cost of attack, while the hackers’ information sharing and profit decrease. Our analysis also reveals the interesting result that the cumulative attack level of the hackers is not affected by the effectiveness of information sharing between them and moreover, is also unaffected by the intensity of joint information sharing. We also find that as the effectiveness of information sharing between hackers increases relative to the investment in attack, the firm’s investment in cyber security defense and profit are constant, the hackers’ investments in attacks decrease, and information sharing levels and hacker profits increase. In contrast, as the intensity of joint information sharing increases, while the firm’s investment in cyber security defense and profit remain constant, the hackers’ investments in attacks increase, and the hackers’ information sharing levels and profits decrease. Increasing the firm’s asset causes all the variables to increase linearly, except information sharing which is constant. We extend our analysis to endogenize the firm’s asset and this analysis largely confirms the preceding analysis with a fixed asset. We use the software Mathematica 10.1 (www.wolfram.com) to program the model mathematically with equilibrium constraints, and perform numerical analysis illustrated graphically.