For an exchange economy, under assumptions which did not bring about the existence of equilibrium with dividends as yet, we prove the non-emptiness of the Edgeworth rejective core. Then, via Konovalov (1998, 2005)’s decentralization result, we solve the equilibrium with dividends existence...

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.