In this paper, we develop a new theory that combines matching theory and the graph model for conflict resolution (GMCR). Specifically, we construct GMCR based on a model that matches three players and three teams using the immediate acceptance method, and calculate the stability of each state regarding Nash, GMR, SMR, and SEQ by program. Of the total 216 states, Student 1 achieved equilibrium for all four stability concepts in 92 states, Student 2 achieved equilibrium in 128 states, and Student 3 achieved equilibrium in 128 states. There were 32 ways in which all students were Nash.