R utcor R esearch R eport RUTCOR Rutgers Center for Operations Research Rutgers University 640 Bartholomew Road Piscataway, New Jersey 08854-8003 Telephone: 732-445-3804 Telefax: 732-445-5472 Email: rrr@rutcor.rutgers.edu http://rutcor.rutgers.edu/∼rrr Criteria of solvability of bimatrix games based on excluding certain 2 × 2 subgames Endre Boros 1 Khaled Elbassioni 2 Vladimir Gurvich 3 Kazuhisa Makino 4 Vladimir Oudalov 5 RRR 31-2007,