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Power and efficiency in pillage games

A pillage game is a formal model of Hobbesian anarchy as a coalitional game. The technology of pillage is specified by a power function that determines the power of each coalition as a function of its members and their wealth. A coalition can despoil any other coalition less powerful than itself. The present paper studies the problem of achieving an efficient allocation of resources when the required reallocation changes the distribution of power. For example, land redistribution may increase total production, but may also deprive the original owners of the power they need to compel compensation. In this case the original owners would block the redistribution. Previous work on pillage games has focused on the stable set (von Neumann-Morgenstern solution) as a representation of a stable balance of power. However, the balance of power is typically too delicate to support a efficient allocations. In particular stable sets are necessarily finite. The present paper shows that for certain power functions, a recently developed extension of the stable set, called the legitimate set, can be rich enough to support efficient reallocation with enforceable compensation.