Let X be a convex subset of a locally convex topological vector space, let U⊂X be open with U¯ compact, let F:U¯→X be an upper semicontinuous convex valued correspondence with no fixed points in U¯∖U, let P be a compact absolute neighborhood retract, and let ρ:U¯→P be a continuous...

A decision scheme (Gibbard, 1977) maps profiles of strict preferences over a set of social alternatives to lotteries over the social alternatives. A decision scheme is weakly strategy-proof if it is never possible for a voter to increase expected utility (for some vNM utility function consistent...

We introduce a combinatorial abstraction of two person finite games in an oriented matroid. We also define a combinatorial version of Nash equilibrium and prove that an odd number of equilibria exists. The proof is a purely combinatorial rendition of the Lemke-Howson algorithm.