Bargaining On Monotonic Economic Environments

Applying the solutions defined in the axiomatic bargaining theory to actual bargaining problems is a challenge when the problem is not described by its Utility Possibility Set (UPS) but as an economic environment specifying the set of alternatives and utility profile underlying the UPS. We introduce the axioms of Independence of Non-Efficient Alternatives and Independence of Redundant Alternatives. A solution satisfying these axioms can be applied to a simplified problem based on any reduced set of alternatives generating the Pareto frontier of the initial problem, and produces the same outcome. We compare our axioms to usual independence axioms, and show that they are satisfied by many usual bargaining solutions. Then, we introduce monotonicity conditions corresponding to the existence of an interest group (i.e., agents ranking the alternatives in the same order). For such monotonic economic environments, we provide a parameterized family of alternatives that generates the Pareto frontier of the bargaining problem, in line with our previous results. Our analysis illustrates that an axiomatic approach can be useful to foster the application of bargaining solutions, in complement to usual computational methods.