Axiomatic theory of bargaining with a variable number of agents - William Thomson

In this book, Professor Thomson and Professor Lensberg extrapolate upon the Nash (1950) treatment of the bargaining problem to consider the situation where the number of bargainers may vary. The authors formulate axioms to specify how solutions should respond to such changes, and provide new characterizations of all the major solutions as well as generalizations of these solutions. The book also contains several other comparative studies of solutions in the context of a variable number of agents. Much of the theory of bargaining can be rewritten within this context. The pre-eminence of the three solutions at the core of the classical theory is confirmed. These are the solutions introducted by Nash (1950) and two solutions axiomatized in the 1970s (Kalai-Smorodinsky and egalitarian solutions).