A repeated imitation model with dependence between stages: Decision strategies and rewards

Adversarial decision making is aimed at determining strategies to anticipate the behavior of an opponent trying to learn from our actions. One defense is to make decisions intended to confuse the opponent, although our rewards can be diminished. This idea has already been captured in an adversarial model introduced in a previous work, in which two agents separately issue responses to an unknown sequence of external inputs. Each agent’s reward depends on the current input and the responses of both agents. In this contribution, (a) we extend the original model by establishing stochastic dependence between an agent’s responses and the next input of the sequence, and (b) we study the design of time varying decision strategies for the extended model. The strategies obtained are compared against static strategies from theoretical and empirical points of view. The results show that time varying strategies outperform static ones.