Predicting the effects of intervention and sabotage in a bounded complex game (Q1196273)

Conditions for predicting the effects of intervention with certainty are derived. An outside observer studies sequences of actions from a two- person repeated prisoners' dilemma. The sequences are generated by finite automata, which are optimal at each stage of the game and also minimise the number of states. An intervention is a change of action for one of the players and a prediction is a statement about what action the other player will choose in the next period. The outside observer makes a sabotage when he sends deceitful information to one of the players about the other player's choice in the previous period. One result is that although it is in general hard to make such predictions, it can be proven that at least one prediction can always be made certain at some stage of the game. Another result is that predictions of actions denoted as ``defection'' in the prisoners' dilemma can be certain, whereas predictions of actions denoted as ``co-operation'' can never be made certain.