Skills, Efficiency, and Timing in a Simple Attack and Defense Model

In this paper, we consider a simple two-player attack and defense model, focusing on the role of players’ abilities and choice timing. Abilities are divided into skills and efficiency, where the former is an absolute notion and the latter a relative notion of ability. Timing is investigated by comparing players’ investments in a simultaneous and a Stackelberg game. In the simultaneous game, the Nash Equilibrium investment level in attack and defense resources is symmetric, increasing in the skills but non-monotonic in the relative efficiency. In the Stackelberg game, the equilibrium investment levels are asymmetric, increasing in the skills, but with their ranking affected only by the relative efficiency. Therefore, interestingly, players’ choice is mostly characterized by players’ relative efficiency rather than by their skills, in regards to timing.