The maximum incentive solutions in bargaining problems

This paper is concerned with a new approach to solutions of bargaining problems, i.e. with a rule by which participants of a nonantagonistic game select, from the set of all feasible outcomes, a ‘fair’ outcome. A rather diverse class of games is considered, and the selection in a concrete game is specified by the class under consideration. Secondly, we introduce a partial ordering on each class of games and imply that this ordering is associated with the ‘contributions of the participants to the game’. The chosen solution depends on this ordering and, in particular, is monotonic with respect to it. Under our preliminary axioms an admissible monotonic solution is not unique, and the problem is to choose a single one. The rule for choosing such a solution is based on the maximum incentive of the participant with the maximum ‘value of his contribution’ but within the framework of postulated axioms, in particular under the monotonicity condition. The latter condition implies that the solution is nontrivial. This paper is devoted to the maximum incentive solution of the so-called Income Allocation Problem and surveys some results related to the general scheme.