Individual monotonicity and the leximin solution
The author introduces to the \(n\)-person bargaining problem two supplementary assumptions due to which he derives new characteristics of the problem. To generally used Pareto efficiency and symmetry of solutions he adds individual monotonicity and independence of individually irrational points. Individual monotonicity means increasing of components of the solution with respect to the number of players. The independence means that if two problems have the same individually rational parts then their solutions coincides. The leximin solution for a two-person game is the Pareto efficient point maximizing the minimum of players' utilities. The author proves that the solution of the two-person game is equal to the leximin solution if and only if all four assumptions are true. The notion of the leximin solution is extended to the \(n\)-person problem and the statement about identity of solution and leximin remains true.
scientific article; zbMATH DE number 1439925