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.
On 9th of April 2018 passed away at the age of 68 after a serious illness, Professor Andrzej Wieczorek -- a respected specialist in the field of operations research, game theory and nonlinear analysis. He is the author of many scientific publications in game theory mainly. We will remember him also as an excellent organizer, lecturer, and researcher. Great colleague, good man.