Abstract Congestion management design is key to a fair and efficient use of transmission facilities and an improvement of market efficiency. Emergence of bilateral electricity markets provides a more flexible, private and decentralized decision-making scenario, in which the self-interested players autonomously search for counterparts to negotiate profitable transactions. In competitive bilateral markets of imperfect and incomplete information and explicit consideration of the network constraints, which make the markets significantly complex, more sophisticated bargaining strategies and market evaluation tools are imperative to both players and regulators. In this paper, under an assumption of imperfect and incomplete information, evolutionary bipartite complex network theory is employed to develop quantities bidding strategies through a dynamic game, in which the players drive the evolution of the network while maximizing their own utilities with explicitly considering the congestion management results. Resorting to adjustment bids, two congestion management schemes, with and without balancing bilateral transactions, are considered. The approach is illustrated with an application to the IEEE30 test system, assessing the impact of different congestion management schemes on the negotiations, market equilibria, market performance and gaming opportunities for the market participants in congestion managements.