Bargaining sets in exchange economies with indivisibilities and money

Abstract

This paper introduces and investigates the semireactive bargaining set (Sudholter and Potters (2001)) and the reactive bargaining set (Granot (1994)), which are originally solution concepts for TU-games, in economies in which agents exchange indivisible goods and one perfectly divisible good (money). Under the assumptions that the preferences of the agents are quasi-linear and the endowments satisfy the Total Abundance condition, a condition on the amounts of money agents initially have, it is shown that the (semi)reactive bargaining set is nonempty. In addition, we prove that in such an economy the (semi)reactive bargaining set and the (strong) core coincide if and only if the (semi)reactive bargaining set and the core of the underlying TU-game coincide.