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Abstract

A distrust operator, describing a kind of agreement among a group of players, transforms any characteristic function game to another game. In this new game, a player from this group can legally access a coalition if and only if all players from the group do the same. A formula for the Shapley value of games obtained by applying distrust operators to one man–one vote majority voting games is given, and the cases in which such an “agreement" is profitable to its parties are discussed. We also prove two theorems concerning the limit behaviour of values of voting games with distrust operators when the number of players tends to infinity but the winning majority percentage remains constant.