The effect of information about strategy on a three-person game

Abstract

When a game of strategy is played by three or more players and coalitions are allowed, the outcome of the game depends on how the players will form coalitions. In the simplest case, the coalition which includes the majority of the players wins the same prize regardless of who is in the winning coalition. In a somewhat more general situation, different “weights” are assigned to different players and a coalition with the preponderant total weight wins. One hypothesis on the formation of coalitions states that if two weaker players can combine their weights to defeat the third stronger player, they will do so. To what extent is this so and under what conditions?