Multi-lateral strategic bargaining without stationarity

This paper establishes existence of subgame perfect equilibrium in pure strategies for a general class of sequential multi-lateral bargaining games, without assuming a stationary setting. The only required hypothesis is that utility functions are continuous on the space of economic outcomes. In particular, no assumption on the space of feasible payoffs is needed. The result covers arbitrary and even time-varying bargaining protocols (acceptance rules), externalities, and other-regarding preferences. As a side result, we clarify the meaning of assumptions on “continuity at infinity.”