We consider a non-cooperative coalitional bargaining game with random proposers in a general situation for which players differ in recognition probability and time preference. We characterize an efficient equilibrium as the generalized Nash bargaining solution that belongs to the core. The model is applied to wage bargaining between an employer and multiple workers. Although involuntary unemployment may occur in equilibrium, full employment emerges as players become sufficiently patient. We analyze a non-cooperative coalitional bargaining game with random proposers. ► The existence of a stationary subgame perfect equilibrium (SSPE) is proved. ► An efficient SSPE allocation is the generalized Nash bargaining solution in the core. ► The model is applied to wage bargaining among one employer and workers. ► Involuntary unemployment may occur.