Disagreement point axioms and the egalitarian bargaining solution

We provide new characterizations of the egalitarian bargaining solution on the class of strictly comprehensive n-person bargaining problems. The main axioms used in all of our results are Nash’s IIA and disagreement point monotonicity—an axiom which requires a player’s payoff to strictly increase in his disagreement payoff. For n = 2 these axioms, together with other standard requirements, uniquely characterize the egalitarian solution. For n > 2 we provide two extensions of our 2-person result, each of which is obtained by imposing an additional axiom on the solution. Dropping the axiom of anonymity, strengthening disagreement point monotonicity by requiring player i’s payoff to be a strictly decreasing function of the disagreement payoff of every other player j ≠ i, and adding a “weak convexity” axiom regarding changes of the disagreement point, we obtain a characterization of the class of weighted egalitarian solutions. This “weak convexity” axiom requires that a movement of the disagreement point in the direction of the solution point should not change the solution point. We also discuss the so-called “transfer paradox” and relate it to this axiom.     

On the implementation of the L-Nash bargaining solution in two-person bargaining games

The “Nash program” initiated by Nash (Econometrica 21:128–140, 1953) is a research agenda aiming at representing every axiomatically determined cooperative solution to a game as a Nash outcome of a reasonable noncooperative bargaining game. The L-Nash solution first defined by Forgó (Interactive Decisions. Lecture Notes in Economics and Mathematical Systems, vol 229. Springer, Berlin, pp 1–15, 1983) is obtained as the limiting point of the Nash bargaining solution when the disagreement point goes to negative infinity in a fixed direction. In Forgó and Szidarovszky (Eur J Oper Res 147:108–116, 2003), the L-Nash solution was related to the solution of multiciteria decision making and two different axiomatizations of the L-Nash solution were also given in this context. In this paper, finite bounds are established for the penalty of disagreement in certain special two-person bargaining problems, making it possible to apply all the implementation models designed for Nash bargaining problems with a finite disagreement point to obtain the L-Nash solution as well. For another set of problems where this method does not work, a version of Rubinstein’s alternative offer game (Econometrica 50:97–109, 1982) is shown to asymptotically implement the L-Nash solution. If penalty is internalized as a decision variable of one of the players, then a modification of Howard’s game (J Econ Theory 56:142–159, 1992) also implements the L-Nash solution.     

Share the gain,share the pain? Almost transferable utility,changes in production possibilities,and bargaining solutions

We consider an n-person economy in which efficiency is independent of distribution but the cardinal properties of the agents’ utility functions may preclude transferable utility (a property we call “Almost TU”). Holding the disagreement point fixed, we show that Almost TU is a necessary and sufficient condition for all agents to either benefit jointly or suffer jointly with any change in production possibilities under well-behaved generalized utilitarian bargaining solutions (of which the Nash bargaining and the utilitarian solutions are special cases). We apply the result to policy analysis and to incentive compatibility.     

Share the gain, share the pain? Almost transferable utility, changes in production possibilities, and bargaining solutions

We consider an n-person economy in which efficiency is independent of distribution but the cardinal properties of the agents’ utility functions may preclude transferable utility (a property we call “Almost TU”). Holding the disagreement point fixed, we show that Almost TU is a necessary and sufficient condition for all agents to either benefit jointly or suffer jointly with any change in production possibilities under well-behaved generalized utilitarian bargaining solutions (of which the Nash bargaining and the utilitarian solutions are special cases). We apply the result to policy analysis and to incentive compatibility.     

The Tempered Aspirations solution for bargaining problems with a reference point

Gupta and Livne (1988) modified Nash’s (1950) original bargaining problem through the introduction of a reference point restricted to lie in the bargaining set. Additionally, they characterized a solution concept for this augmented bargaining problem. We propose and axiomatically characterize a new solution concept for bargaining problems with a reference point: the Tempered Aspirations solution. In Kalai and Smorodinsky (1975), aspirations are given by the so called ideal or utopia point. In our setting, however, the salience of the reference point mutes or tempers the negotiators’ aspirations. Thus, our solution is defined to be the maximal feasible point on the line segment joining the modified aspirations and disagreement vectors. The Tempered Aspirations solution can be understood as a “dual” version of the Gupta–Livne solution or, alternatively, as a version of Chun and Thomson’s (1992) Proportional solution in which the claims point is endogenous. We also conduct an extensive axiomatic analysis comparing the Gupta–Livne to our Tempered Aspirations solution.     

Efficiency-free characterizations of the Kalai–Smorodinsky bargaining solution

Roth (1977) axiomatized the Nash (1950) bargaining solution without Pareto optimality, replacing it by strong individual rationality in Nash’s axiom list. In a subsequent work (Roth, 1979) he showed that when strong individual rationality is replaced by weak individual rationality, the only solutions that become admissible are the Nash and the disagreement solutions. In this paper I derive analogous results for the Kalai–Smorodinsky (1975) bargaining solution.     

The ordered field property and a finite algorithm for the Nash bargaining solution

This note proves that the two person Nash bargaining theory with polyhedral bargaining regions needs only an ordered field (which always includes the rational number field) as its scalar field. The existence of the Nash bargaining solution is the main part of this result and the axiomatic characterization can be proved in the standard way with slight modifications. We prove the existence by giving a finite algorithm to calculate the Nash solution for a polyhedral bargaining problem, whose speed is of orderBm(m-1) (m is the number of extreme points andB is determined by the extreme points).     

Divide the dollar and conquer more: sequential bargaining and risk aversion

We analyze the problem of dividing a fixed amount of a single commodity between two players on the basis of the Nash bargaining solution (NBS). For one-shot negotiations, a cornerstone result of Roth (Axiomatic models of bargaining. Springer, Berlin, 1979) establishes that the more risk averse player will obtain less than half the total amount. In the present paper, we assume that the bargaining procedure occurs over several rounds. In each round, an increasing share of the total amount is negotiated over in accordance with the NBS, the disagreement point being determined by the outcome of the previous round. In line with Roth’s result, the final amount received by the more risk averse player is still bounded by half the total amount. As a new feature, however, this player does not lose from bargaining for more rounds if his opponent exhibits non-increasing absolute risk aversion. What is more, both players’ risk profiles become essentially irrelevant if successive bargaining takes place over sufficiently small commodity increments. Each player then gets approximately half of the commodity.     

A Wiener-type condition for Hölder continuity for Green's functions

Summary We investigate local properties of the Green function of the complement of a compact set Ein R^d, d>2. We give a Wiener type characterization for the H?lder continuity of the Green function, thus extending a result of L. Carleson and V. Totik. The obtained density condition is necessary, and it is sufficient as well, provided Esatisfies the cone condition. It is also shown that the H?lder condition for the Green function at a boundary point can be equivalently stated in terms of the equilibrium measure and the solution to the corresponding Dirichlet problem. The results solve a long standing open problem -- raised by Maz'ja in the 1960's -- under the simple cone condition.     

Paths leading to the Nash set for nonsmooth games

Maschler, Owen and Peleg (1988) constructed a dynamic system for modelling a possible negotiation process for players facing a smooth n-person pure bargaining game, and showed that all paths of this system lead to the Nash point. They also considered the non-convex case, and found in this case that the limiting points of solutions of the dynamic system belong to the Nash set. Here we extend the model to i) general convex pure bargaining games, and to ii) games generated by “divide the cake” problems. In each of these cases we construct a dynamic system consisting of a differential inclusion (generalizing the Maschler-Owen-Peleg system of differential equations), prove existence of solutions, and show that the solutions converge to the Nash point (or Nash set). The main technical point is proving existence, as the system is neither convex valued nor continuous. The intuition underlying the dynamics is the same as (in the convex case) or analogous to (in the division game) that of Maschler, Owen, and Peleg. Received August 1997/Final version May 1998     

The newton filtration and d-determination of bifurcation problems related to C0 contact equivalence

In this paper, from the Newton filtration’s point of view, we construct the singular Riemannian metric and use the method in singular theory to study the bifurcation problems, and give the sufficient condition of d-determination of bifurcation problems with respect to C ⁰ contact equivalence. The special cases of the main result in this paper are the results of Sun Weizhi and Zou Jiancheng.     

关于拟d-Koszul模的一个注记

本文研究了文献[4]中给出的极小马蹄型引理成立的充分条件.借助拟d-Koszul模给出了一个充要条件并给出了一个极小马蹄型引理的应用.     

A remark on the Brézis–Browder theorem in finite dimensional spaces

Brézis and Browder gave an important characterization of maximal monotonicity for linear operators, in reflexive Banach spaces. In this paper, we show that this characterization also preserves the maximal p-monotonicity, in finite dimensional spaces.     

The Tempered Aspirations solution for bargaining problems with a reference point

Gupta and Livne (1988) modified Nash’s (1950) original bargaining problem through the introduction of a reference point restricted to lie in the bargaining set. Additionally, they characterized a solution concept for this augmented bargaining problem. We propose and axiomatically characterize a new solution concept for bargaining problems with a reference point: the Tempered Aspirations solution. In Kalai and Smorodinsky (1975), aspirations are given by the so called ideal or utopia point. In our setting, however, the salience of the reference point mutes or tempers the negotiators’ aspirations. Thus, our solution is defined to be the maximal feasible point on the line segment joining the modified aspirations and disagreement vectors. The Tempered Aspirations solution can be understood as a “dual” version of the Gupta-Livne solution or, alternatively, as a version of Chun and Thomson’s (1992) Proportional solution in which the claims point is endogenous. We also conduct an extensive axiomatic analysis comparing the Gupta-Livne to our Tempered Aspirations solution.     

Kalai-Smorodinsky Bargaining Solution Equilibria

Multicriteria games describe strategic interactions in which players, having more than one criterion to take into account, don’t have an a-priori opinion on the relative importance of all these criteria. Roemer (Econ. Bull. 3:1–13, 2005) introduces an organizational interpretation of the concept of equilibrium: each player can be viewed as running a bargaining game among criteria. In this paper, we analyze the bargaining problem within each player by considering the Kalai-Smorodinsky bargaining solution (see Kalai and Smorodinsky in Econometrica 43:513–518, 1975). We provide existence results for the so called Kalai-Smorodinsky bargaining solution equilibria for a general class of disagreement points which properly includes the one considered by Roemer (Econ. Bull. 3:1–13, 2005). Moreover we look at the refinement power of this equilibrium concept and show that it is an effective selection device even when combined with classical refinement concepts based on stability with respect to perturbations; in particular, we consider the extension to multicriteria games of the Selten’s trembling hand perfect equilibrium concept (see Selten in Int. J. Game Theory 4:25–55, 1975) and prove that perfect Kalai-Smorodinsky bargaining solution equilibria exist and properly refine both the perfect equilibria and the Kalai-Smorodinsky bargaining solution equilibria.     

Endogenous reference points in bargaining

We allow the reference point in (cooperative) bargaining problems with a reference point to be endogenously determined. Two loss averse agents simultaneously and strategically choose their reference points, taking into consideration that with a certain probability they will not be able to reach an agreement and will receive their disagreement point outcomes, whereas with the remaining probability an arbitrator will distribute the resource by using (an extended) Gupta–Livne bargaining solution (Gupta and Livne in Manag Sci 34:1303–1314, 1988). The model delivers intuitive equilibrium comparative statics on the breakdown probability, the loss aversion coefficients, and the disagreement point outcomes.     

A characterization of a limit solution for finite horizon bargaining problems

We investigate a two-person random proposer bargaining game with a deadline. A bounded time interval is divided into bargaining periods of equal length and we study the limit of the subgame perfect equilibrium outcomes as the number of bargaining periods goes to infinity while the deadline is kept fixed. This limit is close to the discrete Raiffa solution when the time horizon is very short. If the deadline goes to infinity the limit outcome converges to the time preference Nash solution. Regarding this limit as a bargaining solution under deadline, we provide an axiomatic characterization.     

Dynamics and axiomatics of the equal area bargaining solution

We present an alternative formulation of the two-person equal area bargaining solution based on a dynamical process describing the disagreement point set. This alternative formulation provides an interpretation of the idea of equal concessions. Furthermore, it leads to an axiomatic characterization of the solution. Received: November 1998/Revised version: September 1999     

Multilateral non-cooperative bargaining in a general utility space

We consider an n-player bargaining problem where the utility possibility set is compact, convex, and stricly comprehensive. We show that a stationary subgame perfect Nash equilibrium exists, and that, if the Pareto surface is differentiable, all such equilibria converge to the Nash bargaining solution as the length of a time period between offers goes to zero. Without the differentiability assumption, convergence need not hold.     

On the bargaining set, kernel and core of superadditive games

We prove that for superadditive games a necessary and sufficient condition for the bargaining set to coincide with the core is that the monotonic cover of the excess game induced by a payoff be balanced for each imputation in the bargaining set. We present some new results obtained by verifying this condition for specific classes of games. For N-zero-monotonic games we show that the same condition required at each kernel element is also necessary and sufficient for the kernel to be contained in the core. We also give examples showing that to maintain these characterizations, the respective assumptions on the games cannot be lifted. Received: March 1998/Revised version: December 1998