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
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M.O.L. Bacharach et al. (eds.J, Epistemic Logic and the Theory of Games and Decisions, 293-302.
© 1997 Kluwer Academic Publishers.