Games of Status

A status game is a cooperative game in which the outcomes are rank orderings of the players. They are a good model for certain situations in which players care about how their “status” compares with that of other players. We present several formal models within this class. Included are authoritarian status games (where coalitions may assign positions in the rank ordering to nonmembers) and oligarchic status games (where they are unableto do so). We consider the issues of a value concept for authoritarian games and that of core existence for oligarchic games. We then add a transferable resource to the models, obtaining “games of wealth and status.” Finally, we consider an interesting variant, called a “secession game,” where coalitions have the right to secede from the grand coalition and form their own smaller “subsocieties,” each with its own hierarchy.