The Egalitarian Solution for Multi-Choice Games

In a multichoice game a coalition is characterized by the level at which each player is acting, and to each coalition a real number is assigned. A multichoice solution assigns, for each multichoice game, a numerical value to each possible activity level of each player, intended to measure the contribution of each such level to reaching the grand coalition in which each player is active at the maximal level. The paper focuses on the egalitarian multichoice solution, characterized by the properties of efficiency, zero contribution, additivity, anonymity, and level symmetry. The egalitarian solution is also shown to satisfy the property of marginalism: it measures the effect of lowering, ceteris paribus, a certain activity level by one. The solution is compared to a multichoice solution studied in klijn, slikker, and zarzuelo (1999). Finally, it is discussed how the formalism of this paper can be applied to the different framework of multi-attribute utilities.