Abstract: Abstract * 1Animals can derive leverage over others from (a) resource holding power, based for instance on fighting ability or dominance, and (b) the possession of commodities, such as special skills and resources that cannot be taken away by force. * 2We contend that power based on the possession of commodities strongly depends on the level of supply and demand for that commodity, a phenomenon we call the ‘market effect’. * 3Several theoretical and empirical examples are given of social systems in which animals belong to two distinct classes that offer two different kinds of commodities. * 4The relative frequency of occurrence of the two classes is shown to determine the relative power of their members. * 5We consider the theoretical properties of bargaining processes by which relative power is converted into corresponding pay-off distributions. * 6We propose coalition games, a class of games with more than two players and in which bargaining is possible, as suitable paradigms for collaboration among members of social units.