Strategic Alliances in Coalitional Bargaining

To analyze players' strategic alliance behavior, we introduce a new noncooperative coalitional bargaining model, in which each player can buy out other players with upfront transfers. We uncover the role of an essential player in a transferable utility game, or a veto player in a simple game, in preventing efficient outcomes and we show that delay in bargaining generically occurs. In an application to legislative bargaining with vote buying, if a veto player and a non-veto player coexist, then a non-winning coalition forms as an intermediate bargaining step and the final winning coalition is not necessarily minimal. In three-player simple games, we fully characterize the set of the equilibrium outcomes, which is equivalent to the convex hull of the core and the egalitarian solution. As the set of equilibrium outcomes includes well-known cooperative power indices, players' strategic alliance can be viewed as a noncooperative foundation of the cooperative solutions.