Determining a Nash equilibrium in a 2-player non-zero sum game is known to be PPAD-hard (Chen and Deng, 2006 [5], Chen, Deng and Teng 2009 [6]). The problem, even when restricted to win-lose bimatrix games, remains PPAD-hard (Abbott, Kane and Valiant, 2005 [1]). However, there do exist polynomial time tractable classes of win-lose bimatrix games such as, very sparse games (Codenotti, Leoncini a...