It should be emphasized that bargaining-game solutions that (like the Nash and Harsanyi solutions) depend on a clearly recognized zero point—that is, on an unambiguous outcome that reigns in the absence of overt agreement—cannot necessarily be applied to a cooperative game that is based on a matrix of choices. A matrix (unless perhaps all payoffs are zero except in the diagonal) does not have a zero point defined by the rules. There is consequently no “normal form” consisting of a convex region and associated zero point unless there is available a fully adequate theory that “solves” the tacit game (and does so in a manner that the players can take for granted). One may, following Luce and Raiffa (for example, page 137) take the players’ “security levels” (maximin values) as the zero point; but this is either arbitrary or based on the hypothesis that, left to themselves, the players could succeed in doing no better than this in the tacit game. The latter hypothesis, especially where there are pure-strategy efficient points (as in Braithwaite’s game, and as in the Luce-Raiffa matrix discussed in note 18 below), is a weak hypothesis that can be empirically refuted; it assumes that rational players are incapable of correlating strategies without communicating, while in fact this is something they often can do even in the face of conflicting preferences.

DEFINE: Clarifies the distinction between bargaining games with a recognized zero point and cooperative games on choice matrices that lack one.

Thomas C. Schelling, The Strategy of Conflict, loc. 851