Stable sets in majority pillage games

Abstract

A pillage game is a coalitional game in which any coalition can take all or part of the wealth of any less powerful coalition. Such an action is called pillage. In the majority pillage game, coalitional wealth contributes to coalitional power, but lexicographically less so than coalitional size. The majority pillage game refines the classic majority game in two respects. First, coalitional wealth can resolve ties in coalitional size. Second, a pillaging coalition need not contain a majority or even half of all of the players in the game. A majority of the players directly affected by the pillage, as winners or losers, is sufficient. This paper characterizes the stable sets of two and three-player games, and the symmetric (permutation invariant) stable sets of games with more than three players. For two or three players, the stable set is unique, and for any odd number of players, the symmetric stable set is unique and equal to the unique symmetric stable set for the classic majority game. If the number of players is even and at least four, no symmetric stable set exists.