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.     

Bankruptcy and the per capita nucleolus: The claim-and-right rules family

This article describes the per capita nucleolus for bankruptcy games as a bankruptcy rule. This rule, called the clights rule, is based on the well-known constrained equal awards principle and it takes into account a vector of clights, a new term which is a blend of claims and rights. These clights only depend on the vector of claims while the height of the estate determines whether the clights should be interpreted as modified claims or as rights. It is shown that both the clights rule and the Aumann–Maschler rule can be captured within the family of so-called claim-and-right rules.     

Rationing problems with ex-ante conditions

An extension of the standard rationing model is introduced. Agents are not only identified by their respective claims to some amount of a scarce resource, but also by some exogenous ex-ante conditions (initial stock of resource or net worth of agents, for instance), other than claims. Within this framework, we define a generalization of the constrained equal awards rule and provide two different characterizations of this generalized rule. Finally, we use the corresponding dual properties to characterize a generalization of the constrained equal losses rule.     

Vigilant measures of risk and the demand for contingent claims

We examine a class of utility maximization problems with a non-necessarily law-invariant utility, and with a non-necessarily law-invariant risk measure constraint. Under a consistency requirement on the risk measure that we call Vigilance, we show the existence of optimal contingent claims, and we show that such optimal contingent claims exhibit a desired monotonicity property. Vigilance is satisfied by a large class of risk measures, including all distortion risk measures and some classes of robust risk measures. As an illustration, we consider a problem of optimal insurance design where the premium principle satisfies the vigilance property, hence covering a large collection of commonly used premium principles, including premium principles that are not law-invariant. We show the existence of optimal indemnity schedules, and we show that optimal indemnity schedules are nondecreasing functions of the insurable loss.     

A noncommutative Brooks-Jewett Theorem

In classical measure theory the Brooks-Jewett Theorem provides a finitely-additive-analogue to the Vitali-Hahn-Saks Theorem. In this paper, it is studied whether the Brooks-Jewett Theorem allows for a noncommutative extension. It will be seen that, in general, a bona-fide extension is not valid. Indeed, it will be shown that a C^*-algebra A satisfies the Brooks-Jewett property if, and only if, it is Grothendieck, and every irreducible representation of A is finite-dimensional; and a von Neumann algebra satisfies the Brooks-Jewett property if, and only if, it is topologically equivalent to an abelian algebra.     

The Euler approximation in state constrained optimal control

We analyze the Euler approximation to a state constrained control problem. We show that if the active constraints satisfy an independence condition and the Lagrangian satisfies a coercivity condition, then locally there exists a solution to the Euler discretization, and the error is bounded by a constant times the mesh size. The proof couples recent stability results for state constrained control problems with results established here on discrete-time regularity. The analysis utilizes mappings of the discrete variables into continuous spaces where classical finite element estimates can be invoked.

     

Merge-proofness in minimum cost spanning tree problems

In the context of cost sharing in minimum cost spanning tree problems, we introduce a property called merge-proofness. This property says that no group of agents can be better off claiming to be a single node. We show that the sharing rule that assigns to each agent his own connection cost (the Bird rule) satisfies this property. Moreover, we provide a characterization of the Bird rule using merge-proofness.     

DIFFEOMORPHISMS WITH VARIOUS C1 STABLE PROPERTIES

Let M be a smooth compact manifold and Λ be a compact invariant set.In this article,we prove that,for every robustly transitive set Λ,f|Λ satisfies a C1-genericstable shadowable property (resp.,C1-gene...     

An alternative characterization of the deferred acceptance algorithm

Kojima and Manea (Econometrica 78(2):633–653, 2010) present two characterizations of when an allocation rule corresponds to the agent-proposing deferred acceptance (DA) algorithm for some substitutable priority rule of the objects being assigned. Building on their results we characterize when an allocation rule is outcome equivalent to the DA algorithm for every substitutable priority rule. In particular, an assignment rule satisfies mutual best (MB) if an agent is always assigned her most preferred object whenever she has the highest priority for it. This mild requirement is a necessary but far from sufficient condition for an assignment rule to be stable. We demonstrate that any allocation mechanism that satisfies MB along with non-wastefulness, population monotonicity and either individually rational monotonicity or weak Maskin monotonicity not only is a stable assignment mechanism but is equivalent to the agent proposing DA algorithm.     

阿罗不可能性定理的几个等价形式

在这篇短中。给出了关于社会福利函数F的防止策略性操纵的概念,并且证明了如果备选对象至少有三个。则下面结论是相互等价的：(1)F满足Pareto与IIA性质;(2)F满足Pareto与RID性质;(3)F是独裁的;(4)F是满的、正向响应的;(5)F是防止策略操纵的且F是满的。     

On the Schröder–Bernstein property for modules

The well known Schröder–Bernstein Theorem states that any two sets with one to one maps into each other are isomorphic. The question of whether any two (subisomorphic or) direct summand subisomorphic algebraic structures are isomorphic, has long been of interest. Kaplansky asked whether direct summands subisomorphic abelian groups are always isomorphic? The question generated a great deal of interest. The study of this question for the general class of modules has been somewhat limited. We extend the study of this question for modules in this paper. We say that a module Msatisfies the Schröder–Bernstein property (S-B property) if any two direct summands of M which are subisomorphic to direct summands of each other, are isomorphic. We show that a large number of classes of modules satisfy the S-B property. These include the classes of quasi-continuous, directly finite, quasi-discrete and modules with ACC on direct summands. It is also shown that over a Noetherian ring R, every extending module satisfies the S-B property. Among applications, it is proved that the class of rings R for which every R-module satisfies the S-B property is precisely that of pure-semisimple rings. We show that over a commutative domain R, any two quasi-continuous subisomorphic R-modules are isomorphic if and only if R is a PID. We study other conditions related to the S-B property and obtain characterizations of certain classes of rings via those conditions. Examples which delimit and illustrate our results are provided.     

The {2}-inverse with applications in statistics

An inverse G of a given matrix A which satisfies the property GAG = G is known as a {2}-inverse. This paper presents a three-phase inversion procedure for which the {2}-inverse is a special case. We present the geometry of {2}-inverses and show that, starting from {2}-inverses, various types of generalized inverses can be derived. Two examples of the occurrence of {2}-inverses in statistics are given: one concerning the constrained least-squares estimator, the other concerning a necessary and sufficient condition for a quadratic form of singular multivariate normal variates to follow a chi-square distribution.     

A characterization of the uniform rule based on new robustness properties

We study the problem of allocating a divisible good among a group of people. Each person’s preferences are single-peaked. We consider situations in which there might be more of the resource to be assigned than was planned, or there might be less of the resource. Two robustness properties are formulated, which we call one-sided composition up and one-sided composition down. We show that only one rule satisfies irrelevance of null agents, the equal-division lower bound, and our robustness properties. This rule is the uniform rule.     

A priori ratemaking using bivariate Poisson regression models

In automobile insurance, it is useful to achieve a priori ratemaking by resorting to generalized linear models, and here the Poisson regression model constitutes the most widely accepted basis. However, insurance companies distinguish between claims with or without bodily injuries, or claims with full or partial liability of the insured driver. This paper examines an a priori ratemaking procedure when including two different types of claim. When assuming independence between claim types, the premium can be obtained by summing the premiums for each type of guarantee and is dependent on the rating factors chosen. If the independence assumption is relaxed, then it is unclear as to how the tariff system might be affected. In order to answer this question, bivariate Poisson regression models, suitable for paired count data exhibiting correlation, are introduced. It is shown that the usual independence assumption is unrealistic here. These models are applied to an automobile insurance claims database containing 80,994 contracts belonging to a Spanish insurance company. Finally, the consequences for pure and loaded premiums when the independence assumption is relaxed by using a bivariate Poisson regression model are analysed.     

On local spectral properties of complex symmetric operators

In this paper we study properties of complex symmetric operators. In particular, we prove that every complex symmetric operator having property (β) or (δ) is decomposable. Moreover, we show that complex symmetric operator T has Dunford?s property (C) and it satisfies Weyl?s theorem if and only if its adjoint does.     

On inductively minimal geometries that satisfy the intersection property

We prove that, up to isomorphism, for a given positive integer n, there is only one inductively minimal pair (Γ,Sym(n)) of rank n-1 that satisfies the intersection property. Moreover, we show that the diagram of Γ is linear.     

Optimal bounds for the no-show paradox via SAT solving

One of the most important desirable properties in social choice theory is Condorcet-consistency, which requires that a voting rule should return an alternative that is preferred to any other alternative by some majority of voters. Another desirable property is participation, which requires that no voter should be worse off by joining an electorate. A seminal result by Moulin (1988) has shown that Condorcet-consistency and participation are incompatible whenever there are at least 4 alternatives and 25 voters. We leverage SAT solving to obtain an elegant human-readable proof of Moulin’s result that requires only 12 voters. Moreover, the SAT solver is able to construct a Condorcet-consistent voting rule that satisfies participation as well as a number of other desirable properties for up to 11 voters, proving the optimality of the above bound. We also obtain tight results for set-valued and probabilistic voting rules, which complement and significantly improve existing theorems.     

A composite run-to-the-bank rule for multi-issue allocation situations

In this paper, we propose a new extension of the run-to-the-bank rule for bankruptcy situations to the class of multi-issue allocation situations. We show that this rule always yields a core element and that it satisfies self-duality. We characterise our rule by means of a new consistency property, issue-consistency.     

Properties of matroids characterizable in terms of excluded matroids

Some properties π of matroids are characterizable in terms of a set S(π) of exluded matroids, that is, a matroid M satisfies property π if and only if M has no minor (series-minor, parallel-minor) isomorphic to a matroid in S(π). This note presents a necessary and sufficient condition for a property to be characterizable in terms of excluded 3-connected matroids.     

Finite character of finitely stable domains

A commutative domain is finitely stable if every nonzero finitely generated ideal is stable, i.e. invertible over its endomorphism ring. A domain satisfies the local stability property provided that every locally stable ideal is stable.We prove that a finitely stable domain satisfies the local stability property if and only if it has finite character, that is every nonzero ideal is contained in at most finitely many maximal ideals. This result allows us to answer the open problem of whether every Clifford regular domain is of finite character.