Abstract: Game theory has been applied widely to interpret and solve the complex and interrelated decision problems．There are few results on non-real valued domain game．This paper investigated two person zero-sum matrix games with lattice-valued payoffs．New equilibrium solutions,i.e．pure strategy Nash equilibrium solution and quasi equilibrium solution,mixed strategy Nash equilibrium solution and quasi equilibrium solution were defined based on the specificity of this kind of game．The properties of equilibrium solutions were studied．The approaches of obtaining equilibrium solutions were proposed．The sufficient and necessary conditions that strategies are the equilibrium solutions were given．Finally,an example was shown to verify the feasibility and effectiveness of the new method dealing with the two person zero-sum matrix games with lattice-valued payoffs.

Key words: Matrix games,Equilibrium solution,Lattice-valued payoffs,Uncertain payoffs