Lgs 8 & 8 Ppcgt

We study the possibility of prediction/decision making in a finite 2-person game with pure strategies, following the Nash-Johansen noncooperative solution theory. We adopt the infinite-regress logic EIR (a fixed-point extension of the epistemic logic KD with 2 persons) to capture individual decision making from the viewpoint of logical inference. In the logic EIR, prediction/decision making is described by the belief set. Our results on prediction/decision making differ between solvable and unsolvable games. For the former, we show that player i can decide whether each of his strategies is a final decision or not. For the latter, we obtain undecidability, i.e., he can neither decide some strategy to be a possible decision nor disprove it. Thus, the theory which is the pair of EIR and the belief set for player i is incomplete in the sense of Goedel's incompleteness theorem for an unsolvable game. This result is related to self-referential, but its main source is a discord generated by interdependence of payoffs and independent prediction/decision making.