13 RATIONALLY JUSTIFIABLE PLAY AND THE THEORY OF NONCOOPERATIVE GAMES R. Cubitt and R. Sugden 13.1 INTRODUCTION Noncooperative game theory is often interpreted as a theory of how games would be played if players were rational. On this view, its central project is to discover which strategies are rationally justifiable and which are not, in any game. In this paper, we consider whether the conventional assumptions of modern game theory equip it to fulfil this project. We present an impossibility result which concerns the extent to which they can do so. The result can be seen as strengthening a claim established by Borgers and Samuelson (1992) and Samuelson (1992). 13.2 AN IMPOSSIBILITY RESULT We will consider finite, normal form, noncooperative games; the set of all such games is denoted by G. We shall say that a strategy is justifiable for a player if and only if it would be an optimal choice for her, given some coherent set of beliefs. A set of beliefs is coherent if and only if it is internally consistent and 293 M.O.L. Bacharach et al. (eds.J, Epistemic Logic and the Theory of Games and Decisions, 293-302. © 1997 Kluwer Academic Publishers.