The paper firstly develops the general strategies of biform games, proposes the concept of common knowledge Nash equilibrium (CKNE), and then presents the proof of its existence. The paper proposes other three forms of equilibriaalmost common knowledge Nash equilibrium(ACKNE), part Common knowledge Nash equilibrium(PCKNE) and part almost common knowledge Nash equilibrium(PACKNE), and gives some examples. It also analyzes the efficiencies of different equilibria. Research results show that the distribution of benefit in CKNE is partly decided by the information itselfa special form of competition environment, and it is efficient. The efficiency of three other forms of equilibria is lower than CKNE, but still higher than Nash equilibrium(NE) of biform games. The four developed forms of biform games’ equilibria can provide methods and theoretical explanation for organizing more efficient cooperation.