Infinite Regresses Arising from Prediction/Decision Making in Games ∗† Tai-Wei Hu‡and Mamoru Kaneko§

We study infinite regresses arising from prediction/decision-making in an -person game, taking beliefs and inferences explicitly into account. We adopt epis-temic logic GL which is an infinitary extension of KD in order to facilitate our discussions on infinite regresses. As a KD-type epistemic logic, we can distinguish between subjectivity and objectivity. In GL we formulate an infinite regress as a formula, and derive its basic properties. In particular, we show that when we add Axiom T (truthfulness) to GL our concept of infinite regress, which is de-fined in a subjective manner, collapses to the common knowledge concept, which is an objective concept. Then we give an epistemic axiomatization of the Nash (noncooperative) solution theory using our concept of infinite regress. Under the assumption of interchangeability, we obtain a full characterization of possible final decisions and predictions for the Nash theory