Problems of fair division and the egalitarian solution: a reconsideration

Abstract

The present paper attempts to provide simple proofs of two theorems in the literature of axiomatic bargaining with a variable population. Both theorems deal with axiomatic characterizations of the egalitarian solution due to Kalai (1997), in the variable population framework. The egalitarian solution assigns to a bargaining problem (arising out of the problem of dividing a bundle of goods amongst a finite number of agents) the utility allocation which is both Weakly Pareto Optimal and has equal coordinates. There are several exhaustive treatments of the central issues in axiomatic bargaining with a variable population, notably Thomson and Lensberg (1985). The origins of this line of speech can be traced to Thomson (1983a).