Euler Complexes (Oiks)

We present a class of instances of the existence of a second object of a specified type, in fact, of an even number of objects of a specified type, which generalizes the existence of an equilibrium for bimatrix games. The proof is an abstract generalization of the Lemke-Howson algorithm for finding an equilibrium of a bimatrix game. ns of this note, with various examples, were presented at a Dagstuhl conference in 2007, the Dubrovnik ECCO XXI conference in 2008, the Paris TGGT conference in 2008, and the Bonn conference, “Recent trends in Combinatorial Optimization”, proceedings: Springer, 2009. The version here is meant to be updated convenience for the session on Oiks, ISCO, 2010.