Axiomatic Theory of Bargaining with a Variable Number of Agents

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).

Acknowledgments; 1. Preliminaries; 2. Axiomatic theory of bargaining with a fixed number of agents; 3. Population monotonicity and the Kalai-Smorodinsky solution; 4. Population monotonicity and the egalitarian solution; 5. Truncated egalitarian and monotone path solutions; 6. Guarantees and opportunities; 7. Stability and the Nash solution; 8. Stability without pareto-optimality; 9. Stability and the leximin solution; 10. Population monotonicity, weak stability and the egalitarian solution; 11. Stability and collectively rational solutions; 12. Invariance under replication and juxtaposition; Bibliography; Index.

This book extrapolates on 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 the generalizations of these solutions.