Stable Demands and Bargaining Power in Majority Games

This paper provides a co-operative as well as a non-cooperative analysis of weighted majority games. The co-operative solution concept introduced here, the Stable Demand Set, yields a meaningful selection within the Mas-Colell Bargaining Set, it contains the Core, it eliminates the "dominated" coalition structures, and has sharp implications for weighted majority games: for such games it is non-empty, it predicts a unique stable demand vector for every homogeneous representation, and every agent within the winning coalition is expected to obtain a payoff share proportional to her relative bargaining power. The set of stable demand vectors coincides with the set of balanced aspirations defined in Bennet (1983), but it is obtained in the space of individually rational payoff configurations, rather than restricting attention to the aspirations domain. I then define two different kinds of non-cooperative coalitional bargaining games, showing that the set of Symmetric Stationary Subgames Perfect Equilibria of one of them, and the set of Subgame Perfect Equilibria of the other, have a one-to-one correspondence with the Stable Demand Set for homogeneous weighted majority games.