We propose a new solution for coalition bargaining problems among n players that can form coalitions c generating heterogenous coalitional values ▪. The players' values vi and probability of coalition formation ▪ are given by: Display omitted where coalition c is chosen only if it maximizes the average gain ▪ and ▪. This solution is the strong Markov perfect equilibrium of a non-cooperative coalition bargaining game where players choose simultaneously the coalition they want to join followed by negotiations to split the surplus. The solution does not rely on the specification of a proposer recognition protocol. For majority voting games, the solution exhibits more inequality among the values of large and small parties and a concentrated equilibrium coalition formation distribution.