Cooperative strategic games

We present a solution concept, called the value, for n-person strategic games with complete or incomplete information (Bayesian games). The value provides an a priori evaluation of the economic worth of the position of each player; it reflects the players' strategic possibilities, including their ability to selectively share information and to make threats against one another. In the special case of games with complete information the value coincides with a solution developed by Shapley, Nash, and Harsanyi, and in two-person Bayesian games it coincides with a solution developed by Kalai and Kalai. Applications of the value in economics have been rare, at least in part because the existing definition (for $n >2$) consists of an ad hoc scheme that does not easily lend itself to computation. We present a simple formula for computing the value and prove that it is the unique function, from n-player games to n-dimensional vectors of payoffs, that satisfies a short list of desirable properties (axioms).