Phase transitions are being used increasingly to probe the collective behaviors of social human systems. In this study, we propose a different way of investigating such transitions in a human system by establishing a two-sided minority game model. A new type of agents who can actively transfer resources are added to our artificial bipartite resource-allocation market. The degree of deviation from equilibria is characterized by the entropy-like quantity of market complexity. Under different threshold values, Q_th, two phases are found by calculating the exponents of the associated power spectra. For large values of Q_th, the general motion of strategies for the agents is relatively periodic whereas for low values of Q_th, the motion becomes chaotic. The transition occurs abruptly at a critical value of Q_th. Our simulation results were also tested based on human experiments. The results of this study suggest that a chaotic-periodic transition related to the quantity of market information should exist in most bipartite markets, thereby allowing better control of such a transition and providing a better understanding of the endogenous emergence of business cycles from the perspective of quantum mechanics.