Values of majority voting games with distrust operators

Marcin Malawski¹

¹ Institute of Computer Science Ordona 21 01-237 Warszawa, Poland

Applicationes Mathematicae, Tome 29 (2002) no. 1, pp. 117-126.

Résumé

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.

Détail

DOI : 10.4064/am29-1-10

Keywords: distrust operator describing kind agreement among group players transforms characteristic function game another game game player group legally access coalition only players group formula shapley value games obtained applying distrust operators man vote majority voting games given cases which agreement profitable its parties discussed prove theorems concerning limit behaviour values voting games distrust operators number players tends infinity winning majority percentage remains constant