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This paper studies an allocation procedure for coalitional games with veto players. The procedure is similar to the one presented by Arin and Feltkamp (J Math Econ 43:855-870, 2007), which is based on Dagan et al. (Games Econ Behav 18:55-72, 1997). A distinguished player makes a proposal that the remaining players must accept or reject, and conflict is solved bilaterally between the rejector and the proposer. We allow the proposer to make sequential proposals over several periods. If responders are myopic maximizers (i.e. consider each period in isolation), the only equilibrium outcome is the serial rule of Arin and Feltkamp (Eur J Oper Res 216:208-213, 2012) regardless of the order of moves. If all players are fully rational, the serial rule still arises as the unique subgame perfect equilibrium outcome if the order of moves is such that stronger players respond to the proposal after weaker ones

A bargaining procedure leading to the serial rule in games with veto players