The Instability of Minimum Winning Coalitions

Abstract

This paper examines William Riker's thesis that only minimum winning coalitions form in n-person zero-sum symmetric games. It demonstrates that Riker's conclusion is false by identifying the conditions under which larger than minimum winning coalitions can form. Since these conditions are quite general it indicates that Riker's conclusion is valid only for a highly restricted class of games. This class of games is identified as those in which players not in a minimum winning coalition have no incentive to form any coalitions among themselves. These games are characterized as games inessential over coalitions of losers. Only in these games can minimum winning coalitions be expected to form exclusively. In all other games, larger than minimum winning coalitions are possible.