Positive Cones and Nash Equilibria

The probability that a line through the origin pierces the cone generated by n vectors in [Note: See the image of page 583 for this formatted text] R^m chosen with a centrally symmetric distribution is calculated. This is used to derive the probability of the existence of a Nash equilibrium for a random pay-off matrix A, for which p_i is never zero, or is zero for only one component, given some assumptions about the probability distribution of the elements of A.