Youngsub Chun

The proportional solution for rights problems

Abstract Recently there have been several studies to provide axiomatic characterizations of solutions to rights problems. However, these studies do not give a satisfactory answer to the question why the proportional solution is the most widely used. This is the question addressed in this paper. To that purpose, we adopt the axiomatic approach; we suggest a set of axioms which a desirable solution should satisfy and we show that the proportional solution is the only solution to satisfy these axioms. Our main axioms are no advantageous reallocation and additivity . A solution satisfies no advantageous reallocation if no subgroup of claimants ever benefits by transferring parts of their claims between themselves. A solution satisfies additivity if it yields the same allocation whether the total estate is divided at once or in several steps.

BARGAINING PROBLEMS WITH CLAIMS

Abstract We enrich the traditional model of bargaining by adding to the disagreement point and the feasible set a point representing claims (or expectations) that agents may have when they come to the bargaining table. We assume this point to be outside of the feasible set: the claims are incompatible, We look for solutions to the class of problems so defined, using the axiomatic method. We follow the various approaches that have been found useful in the classical axiomatic theory of bargaining. We successively consider how solutions respond to certain changes in (i) the feasible set, (ii) the disagreement point and the claims point, and (iii) the number of agents. In each case we formulate appropriate axioms and study their implications. Surprisingly, each of these approaches leads to the same solution: it is the solution that associates with each problem the maximal point of the feasible set on the line segment connecting the disagreement point to the claims point. We name this solution the proportional solution .

Monotonicity properties of bargaining solutions when applied to economics

Abstract We are concerned with the application of bargaining solutions to economic problems of fair division, and, in particular, with the way they respond to changes in the amount to be divided. For instance, one may want an increase in that amount to benefit all agents. A variety of monotonicity properties have been studied in the abstract framework of bargaining theory. Most of the commonly studied solutions are known not to satisfy many of these properties. Here, we investigate the extent to which they do when applied to economics. We show that when there is only one good, they do in fact satisfy many monotonicity properties that they do not satisfy in general. However, this positive result fails as soon as the number of commodities is greater than 2.

The equal-loss principle for bargaining problems

Abstract We introduce a new bargaining solution, which we call the equal-loss solution. This solution equalizes across agents the losses from the ideal point. Two characterizations of the solution are presented by formulating axioms specifying how bargaining solutions should respond to changes in the feasible set and the ideal point.

Equivalence of axioms for bankruptcy problems

Abstract. The bankruptcy problem is concerned with how to divide the net worth of the bankrupt firm among its creditors. In this paper, we investigate the logical relations between various axioms in the context of bankruptcy. Those axioms are: population-and-resource monotonicity, consistency, converse consistency, agreement, and separability. In most axiomatic models, they are not directly related. However, we show that they are equivalent on the class of bankruptcy problems under minor additional requirements.

A new axiomatization of the shapley value

We consider values for transferable utility coalitional form games. We impose on values the requirements of efficiency, triviality, coalitional strategic equivalence, and fair ranking. Efficiency requires that the payoffs to players exhaust all benefits generated by forming the grand coalition. Triviality requires that all players receive nothing if the game is trivial. Coalitional strategic equivalence requires that an improvement in the technology available to some coalition would not affect the payoffs of the players that do not belong to the coalition. Fair ranking requires that the relative payoffs of players belonging to some coalition be determined by their contributions to other coalitions. We show that these four axioms uniquely characterize the Shapley value.

Bargaining with uncertain disagreement points

MUCH OF THE UNCERTAINTY concerning the likely outcome of a typical management-labor conflict pertains to the cost of possible conflict to the two sides. In this paper, we consider situations of this kind, where the cost of conflict is not known with certainty. However, we will assume the benefits from cooperation to be known. We place our analysis in the abstract framework formulated by Nash (1950): Nash described a bargaining problem as a pair consisting of a feasible set (the amount to be divided among management and labor) and a disagreement point (giving the payoffs to both sides when they fail to reach agreement on a division, that is, the strike). Nash investigated the existence of solutions to such problems that would satisfy a certain list of appealing properties. In his analysis both feasible set and disagreement point were assumed to be known. Here, we assume only the feasible set to be known. Several studies have appeared of bargaining situations where the feasible set is unknown but the disagreement point is known. While we are of course not denying the relevance of such studies, we believe that an analysis of situations where it is the consequences of conflict that are unknown might be equally, and perhaps even more, relevant to industrial experience. Indeed, consider a management-labor conflict over wages and benefits. In many industries, the future profitability of the enterprise can be predicted with reasonable accuracy on the basis of its performance in the previous years, whereas the impact of a strike might depend on a number of factors that are significantly harder to evaluate. This is because strikes are infrequent and conjectures about these factors are often not put to the test (a strike is a threat that is often not carried out), and because they involve a number of parameters that are difficult to quantify, such as the psychological readiness of the strikers, the support they might receive from the population and the media, and the likely response of competing and related industries. We impose on solutions a new condition of disagreement point concavity guaranteeing that agents will agree on a compromise before the uncertainty concerning the disagreement point is resolved. To illustrate this requirement somewhat more concretely, suppose that bargaining takes place today, without the precise location of the disagreement point being known, this uncertainty being resolved tomorrow. The bargainers have two options: the first option is simply to wait until tomorrow and solve then whatever problem has come up. Unfortunately, the resulting pair of contingent compromises, evaluated today, is in general strictly Pareto-dominated. The other possibility is to solve today the problem obtained by replacing the uncertain disagreement point by its expected value (this represents the cost of conflict evaluated today) and to solve the resulting problem today. This second option has the advantage of yielding Paretoundominated compromises (provided, of course, that agents would, in the case of no uncertainty, select such compromises), but unfortunately, it may make one of the agents worse off than under the first option. In order to ensure that all agents agree to reaching a compromise today, we require that the second option always Pareto-dominate the first one. We show that disagreement point concavity, when used in conjunction with three standard properties that are satisfied by virtually all of the solutions commonly discussed

The Solidarity Axiom for Quasi-linear Social Choice Problems

Recently, Moulin gave various axiomatic characterizations of solutions to quasi-linear social choice problems. He used a consistency axiom, which relates solutions for societies of different sizes, in addition to some basic axioms. In this paper, we introduce another axiom relating solutions for societies of different sizes, called the “Solidarity Axiom”. This axiom demands that when additional agents enter the scene, all of the original agents be affected in the same direction, i.e., all of them gain or all of them lose. Our main result is a complete characterization of solutions satisfying the solidarity axiom, in addition to Pareto optimality, anonymity and two normalization axioms. All solutions satisfying these five axioms are in the egalitarian spirit; each solution assigns to every agent an equal share of the surplus over some reference level, but uses a different method to compute the reference level. Then, using additional milder axioms, we give further characterization results concerning various subfamilies.

Nash solution and uncertain disagreement points

Abstract We analyze bargaining problems with known feasible sets but uncertain disagreement points. We investigate the existence of solutions such that, under reasonably restricted circumstances, all agents be as well off by reaching an agreement today as they would be by waiting until the uncertainty is resolved. We use this requirement, together with a few other commonly used conditions, to characterize the Nash solution.

A pessimistic approach to the queueing problem

Abstract Given a group of agents to be served in a facility, the queueing problem is concerned with finding the order in which to serve agents and the (positive or negative) monetary compensations they should receive. Maniquet [F. Maniquet, A characterization of the Shapley value in queueing problems, Journal of Economic Theory 109 (2003), 90–103.] shows that the problem can be solved by applying the Shapley value to the game obtained by defining the worth of each coalition to be the minimum waiting cost incurred by its members under the assumption that they are served before the non-coalitional members. Here, we investigate a pessimistic definition for the worth of a coalition. It is obtained by assuming that the coalitional members are served after the non-coalitional members. Even though we apply the same value to the game, the resulting rule is very different from Maniquets. We develop axiomatic characterizations of the rule.