Attack and Defense Strategies in Cyber War Involving Production and Stockpiling of Zero-Day Cyber Exploits

Abstract

Two players strike balances between allocating resources for defense and production of zero-day exploits. Production is further allocated into cyberattack or stockpiling. Applying the Cobb Douglas expected utility function for equivalent players, an analytical solution is determined where each player’s expected utility is inverse U shaped in each player’s unit defense cost. More generally, simulations illustrate the impact of varying nine parameter values relative to a benchmark. Increasing a player’s unit costs of defense or development of zero-days benefits the opposing player. Increasing the contest intensities over the two players’ assets causes the players to increase their efforts until their resources are fully exploited and they receive zero expected utility. Decreasing the Cobb Douglas output elasticity for a player’s stockpiling of zero-days causes its attack to increase and its expected utility to eventually reach a maximum, while the opposing player’s expected utility reaches a minimum. Altering the Cobb Douglas output elasticities for a player’s attack or defense contests towards their maxima or minima causes maximum expected utility for both players.