A Projective Simulation Scheme for a Partially-Observable Multi-Agent Game

We develop a two-defender (Alice and Bob) invasion game using the projective simulation method as an embodied model for artificial intelligence. We hope that it can be the first step towards the effect of perception on different actions in a given game. As a given perception of a given situation, the agent, say Alice, encounters some attack symbols coming from the right attacker, where she can learn to prevent. However, some of these percepts are invisible for her. Instead, she perceives some other signs that are related to her partner’s (Bob) task. We elaborate on an example in which an agent perceives an equal portion of percepts from both attackers. Alice can choose to concentrate on her job, though she loses some attacks. Alternatively, she can have some sort of cooperation with Bob to get and give help. It follows that the maximum blocking efficiency in concentration is just the minimum blocking efficiency in cooperation. Furthermore, Alice would have a choice to select two different forgetting factors for blocking attacks and for helping task. Therefore, she can choose between herself and the other. Consequently, selfishness is discerned as an only Nash equilibrium in this game. It is a pure strategy and Pareto optimal containing Shapley value in this superadditive coalition. Finally, we propose another perception for the same situation that can be tracked in the future based on the present study.