Theoretical analysis of expected payoff in an adversarial domain

Adversarial decision making is aimed at finding strategies for dealing with an adversary who observes our decisions and tries to learn our behavior pattern. Based on a simple mathematical model, the present contribution provides analytical expressions for the expected payoff when using simple strategies which try to balance confusion and payoff. Additional insights are provided regarding the structure of the payoff matrix. Computational experiments show the agreement between theoretical expressions and empirical simulations, thus paving the way to make the assessment of new strategies easier.