A Path Following Procedure for Finding a Point in the Core of a Balanced N-Person Game

A basic theorem in n-person game theory due to Scarf states that a balanced game has a nonempty core. Scarf's proof presents a procedure to find a point in the core of a discrete game, where every coalition disposes of a finite number of alternatives. The proof for a general game follows by passing to the limit. In this paper we present a procedure which works with the characteristic sets in original form. They no longer need to be approximated. The procedure consists in following a finite sequence of possibly nonlinear paths. The framework adopted for this paper is more general than needed to treat the core problem. This enables us to present a unified approach treating the latter problem as well as related problems in linear complementarity theory and fixed point computation.