Narrow Results

In economic allocation problems, egalitarianism and marginalism are two major thoughts to distribute the benefits of cooperation. The α-CIS value reconciles the two thoughts in some variable extent by a parameter α ∈ [0, 1]. The α-CIS value is the center of gravity of the corresponding α-imputation set given the α-imputation set is nonempty. From the cooperative perspective, we present several axiomatizations of the α-CIS value using α-individual rationality or α-dummifying player property. Finally, we provide a noncooperative interpretation of the α-CIS value by a bidding mechanism.

From a special class of TU games with information cost, given by the problem of sharing the costs of facilities among users, we build a noncooperative game in which every player asks for the assessment of whom the users are. We analyze two models, "naming" game and majority decision game: the existence of equilibria is assured since the games are binary and symmetric, and then potential games. Since the games are ex-ante fair, we search a proposal to compensate for ex-post injustice.

Mathematical foundations of conflict resolutions are deeply rooted in the theory of cooperative and non-cooperative games. While many elementary models of conflicts are formalized, one often raises the question whether game theory and its mathematically developed tools are applicable to actual legal disputes in practice. We choose an example from union management conflict on hourly wage dispute and how zero sum two person game theory can be used by a judge to bring about the need for realistic compromises between the two parties. We choose another example from the 2000-year old Babylonian Talmud to describe how a certain debt problem was resolved. While they may be unaware of cooperative game theory, their solution methods are fully consistent with the solution concept called the nucleolus of a TU game.

We provide axiomatic characterizations of the solutions of transferable utility (TU) games on the fixed player set, where at least three players exist. We introduce two axioms on players’ nullification. One axiom requires that the difference between the effect of a player’s nullification on the nullified player and on the others is relatively constant if all but one players are null players. Another axiom requires that a player’s nullification affects equally all of the other players. These two axioms characterize the set of all affine combinations of the equal surplus division and equal division values, together with the two basic axioms of efficiency and null game. By replacing the first axiom on players’ nullification with appropriate monotonicity axioms, we narrow down the solutions to the set of all convex combinations of the two values, or to each of the two values.