Power, control, and coalition formation

A committee is a group of players which has to make one or more decisions; think about town councils, parliaments or the UN Security Council. The common characteristic of all committees is that some groups of players, coalitions, can impose their will if they work together. There are not many restrictions how these winning coalitions look like. In a parliament it can be a coalition of parties with the absolute majority of seats, in case of the UN Council a winning coalition must contain 9 votes, including those of all permanent members. In any case, we can describe the situation within a committee by the set of winning coalitions. This structure has already been introduced by von Neumann and Morgenstern (1944) under the name simple game. Since then mainly two directions of research emerged. One considered simple games as abstract objects, the other placed them into the the context of social choice: A committee has to choose one out of several possible alternatives. Players have preferences over these alternatives and form coalitions according to their interests. Such models as well as conditions on preferences which guarantee a stable outcome of the game, appeared around the same time.