Efficient Coalitional Bargaining with Noncontingent Offers II : Sequential Proposer Protocol

A new feature pertaining to proposer's ability to implement offers is introduced in the extensive form bargaining mechanism studied in Chatterjee et. al. (1993). This mechanism is used to analyze two classes of coalitional games with transferable utility. One class is that of strictly supermodular games; the other has the property that per capita value is increasing as a coalition adds to its members. The new feature in the mechanism is that the proposer has a choice to implement his proposal with any subset of responders who have accepted it. It is shown that for all coalitional games in either class and for all sufficiently high discount factors, there exists an order-independent efficient subgame perfect equilibrium in pure stationary strategies whose limiting outcome as players get more patient is the core-constrained Nash Bargaining Solution. For strictly supermodular games, Core is a binding constraint on Nash Bargaining Solution while for the other class it is not