Heuristic modeling of reflection in reflexive games

The functioning of a subject in a changing environment is most effective from the point of view of survival if the subject can form, maintain and use internal representations of the external world for decision-making. These representations are also called reflection in a broad sense. Using it, one can win in reflexive games since an internal representation of the enemy allows predicting their future moves. The goal is to assess the reflexive potential of heuristic model objects – artificial neural networks – in the reflexive games “Even-Odd” (or “Matching pennies”) and “Rock-Paper-Scissors”. We used homogeneous fully connected neural networks of small sizes (from 8 to 45 neurons). Games were played between neural networks with different configurations and parameters (size, step size for modifying weight coefficients). A set of reflexivity criteria is presented, corresponding to different levels of consideration: neuronal, behavioral, formal. The transitivity of formal success in the game is shown. The most successful configurations, however, may not meet other criteria of reflexivity. We hypothesize that the best compliance with the criteria and, as a consequence, universal success in reflection tasks is achievable for heterogeneous configurations with a structure in which the formation of hierarchical systems of attractors is possible.