Rational benevolence in small committees

Abstract

We consider a pie-splitting game involving three committee members. In response to the large literature on sequential procedures in this type of game, we propose an institution that is inspired by auction theory. The (sealed) bids of the players are proposals for a distribution of the pie and are given simultaneously. If any of the bids is preferred to all others in a pairwise comparison (i.e. a Condorcet winner exists) then this proposal is implemented. If such a bid does not exist then an equal split of the pie is assumed. An equilibrium of this game is for each player to suggest that one of the opponents should receive the lion’s share of the pie, even though each player cares only about his own share. We call this phenomenon “rational benevolence”. Although the end that is desired by the players is purely egoistic, the means of achieving it may be perceived as benevolent. Several applications of the game are suggested.