Replication invariance on NTU games

Two concepts of replication (conflictual and non-conflictual) are extended from the class of pure bargaining games to the class of NTU games. The behavior of the Harsanyi, Shapley NTU, Egalitarian and Maschler-Owen solutions of the replica games is compared with that of the Nash and Egalitarian solutions in pure bargaining games. Received June 1995/Final version February 2000     

Uncovered bargaining solutions

An uncovered bargaining solution is a bargaining solution for which there exists a complete and asymmetric relation (tournament) such that, for each feasible set, the bargaining solution set coincides with the uncovered set of the tournament. We provide a characterization of a class of uncovered bargaining solutions.     

Continuity of bargaining solutions

Upper semicontinuous solutions of the bargaining problem are studied and also lower semicontinuous weak solutions of that problem are considered. Though mainly compact bargaining pairs are investigated, extensions to non-compact bargaining pairs are indicated. The continuity properties of some well known bargaining solutions are discussed.     

Continuity properties of bargaining solutions

Three different concepts of continuity of bargaining solutions are examined: Pareto continuity, Hausdorff continuity, and Kuratowski continuity. A new axiomatic characterization of the Nash solution is proposed. In this axiomatization, Kuratowski continuity plays a major role.     

Inequality averse multi-utilitarian bargaining solutions

This paper introduces and analyzes the class of inequality averse multi-utilitarian solutions for cooperative bargaining problems. We show that generalized Gini solutions and inequality averse Choquet solutions are particular cases of this new multi-valued solution concept and provide a complete characterization in which an invariance property, consisting of a weakening of both the linear invariance axiom in Blackorby et al. (Econometrica 62:1161–1178, 1994) and the restricted invariance axiom in Ok and Zhou (Games Econ Behav 33:249–264, 2000), plays an important role. Moreover, by relaxing the assumptions involved in the characterization, the class is extended to include inequality loving multi-utilitarian solutions which are also studied in the paper.     

Multiple-issue bargaining and axiomatic solutions

We study two-person, multiple-issue bargaining problems and identify four procedures by which the bargaining may take place. Drawing on some logic from non-cooperative game theory, we propose axioms which relate the outcomes of the procedures. We also promote a weak monotonicity axiom on solutions, called issue-by-issue monotonicity, which is geared toward multiple-issue bargaining. Our main result concerns the relationship between a sequential bargaining procedure — with the rule that agreements are implemented only after all issues are resolved — and global bargaining (in which all issues are negotiated simultaneously). If a bargaining solution predicts the same outcome with these two procedures, then we say that it satisfiesagenda independence. We prove that a solution satisfies axioms of efficiency, symmetry, scale invariance, issue-by-issue monotonicity, and agenda independence if and only if it is the Nash solution. This result provides new intuition for Nash's independence of irrelevant alternatives axiom. Among other results, we show that a solution is invariant to all four of the procedures and satisfies efficiency and symmetry if and only if it is the utilitarian solution with equal weights. We comment on the results of other authors who address multiple-issue bargaining.     

Nonzero-sum differential games with bargaining solutions

Nash's bargaining solution for finite games is extended to differential games with nonzero-sum integral payoffs. Sufficient conditions for the optimality of a strategy pair are established. An example is given.     

Nonsymmetric Nash solutions and replications of 2-person bargaining

A 2-person fixed threat bargaining problem is considered. A full characterization of the solutions which satisfy all of Nash's axioms except for the axiom of symmetry is given. It is also shown that these nonsymmetric Nash solutions are precisely the solutions that arise from symmetric Nash solutions through replications.     

Monotonicity properties of bargaining solutions when applied to economics

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.     

Conditional invariance and exact solutions of the nonlinear equation

The conditional invariance of the nonlinear heat equation is studied. Conditionalinvariance operators are applied for reducing the original equation to ordinary differential equations, and also for finding its exact solutions.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 10, pp. 1370–1376, October, 1990.     

On the relevance of alternatives in bargaining: generalized average pay-off solutions

We generalize the average pay-off solution proposed by Anbarci (Can J Econ 28:675–682, 1995), which depends on all the alternatives, and show that the Nash and Kalai–Smorodinsky solutions are limits of generalized average pay-off solutions. We formalize the notion of relevant alternatives and compare solutions in terms of the relevance of alternatives. I am much indebted to Roberto Serrano for his guidance and many discussions, and William Thomson for his numerous detailed suggestions for improvements. I thank Youngsub Chun, Michael Maschler, Yeneng Sun, Rajiv Vohra, Oscar Volij, Myrna Wooders, an associate editor, anonymous referees, and seminar participants at Brown University, the National University of Singapore, and the 2003 North American Summer Meetings of the Econometric Society for valuable comments. I gratefully acknowledge research support from Brown University through an Eccleston Fellowship award.     

Chapter 4 The lack of invariance of optimal dual solutions under translation

It is shown that optimal dual solutions for the Additive and the BCC models are not invariant under translation. In particular, this implies that the Ali-Seiford (1990) and Pastor (in chapter 3) results on translations apply only to the envelopment portion of DEA and thus do not, in particular, deal fully with domains having nonnegative inputs and outputs (but with no zero input or output vector).R.M. Thrall is Professor of Administration and Noah Harding Professor of Mathematical Sciences, Emeritus, Rice University.     

Flow invariance for solutions to nonlinear nonautonomous partial differential delay equations

We investigate the problem of existence and flow invariance of mild solutions to nonautonomous partial differential delay equations , t?s, us=φ, where B(t) is a family of nonlinear multivalued, α-accretive operators with D(B(t)) possibly depending on t, and the operators F(t,.) being defined—and Lipschitz continuous—possibly only on “thin” subsets of the initial history space E. The results are applied to population dynamics models. We also study the asymptotic behavior of solutions to this equation. Our analysis will be based on the evolution operator associated to the equation in the initial history space E.     

Multiple existence of non-radial solutions with group invariance for sublinear elliptic equations

We deal with sublinear elliptic equations in a ball and prove the existence of infinitely many solutions which are not radially symmetric but G invariant. Here G is any closed subgroup of the orthogonal group and is not transitive on the unit sphere.     

On the fiber structure of symmetry invariance sets of solutions to quasilinear equations

Known results about the unique continuation of solutions of anisotropic linear and weakly nonlinear differential equations and the extension of the invariance property of these solutions are applied to prove theorems about the fiberwise quasianalyticity and the fiber structure of sets of symmetry invariance of solutions to quasilinear equations.     

Weak invariance principle for solutions of stochastic recurrence equations in a banach space

We show that, in a Banach space, continuous random processes constructed by using solutions of the difference equationX _n =A _n X _n+1+V _n , n=1, 2,..., converge in distribution to a solution of the corresponding operator equation.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 1, pp. 114–117, January, 1995.     

Asymptotic behaviors of solutions to evolution equations in the presence of translation and scaling invariance

There are wide classes of nonlinear evolution equations which possess invariant properties with respect to a scaling and translations. If a solution is invariant under the scaling then it is called a self-similar solution, which is a candidate for the asymptotic profile of general solutions at large time. In this paper we establish an abstract framework to find more precise asymptotic profiles by shifting self-similar solutions suitably.