Equilibrium in repeated Stackelberg Public Goods game with two-leaders-one-follower and one-step-memory

Stackelberg game with hierarchical and information structures has broad background and applications in practice. In this paper the repeated Stackelberg Public Goods game with 2 leaders and 1 follower will be investigated, where the leaders´ strategies are with one-step-memory with respect to the follower´s action. The players act simultaneously at each step. By constructing the state transfer graph for given leaders´ strategy profile, the equilibrium of the game can be solved, which can be cooperation or defection if the reward rate is small and is cooperation if the rate is big.