Bargaining with stochastic disagreement payoffs

We study a bargaining model where (i) players interim disagreement payoffs are stochastic and (ii) in any period, the proposer may postpone making an offer without losing the right to propose in the following period. This bargaining model has a generically unique perfect equilibrium payoff for each player, and the equilibrium outcome is inefficient in some cases, featuring a stochastically delayed agreement. We show that both the variation of players interim disagreement payoffs and the proposers ability to postpone making an offer without losing the right to propose are necessary for the existence of such a unique and inefficient perfect equilibrium outcome. Received April 2002/Final version April 2003     

Lexicographic egalitarian solution and uncertainty in the disagreement point

We analyze bargaining situations in which the feasible set is known but the disagreement point is uncertain. By requiring that all agents, generally, be affected by the uncertainty in the same way, we characterize thelexicographic egalitarian solution.Discussions with Professors William Thomson and Hans Peters are gratefully acknowledged. However, I have full responsibility for any shortcomings.     

The equivariant LS-category of polar actions

We will provide a lower bound for arbitrary proper actions in terms of the stratification by orbit types, and an upper bound for proper polar actions in terms of the equivariant LS-category of its generalized Weyl group. As an application we reprove a theorem of Singhof that determines the classical Lusternik-Schnirelmann category for U(n) and SU(n).     

Distinguishing labeling of group actions

Suppose Γ is a group acting on a set X. An r-labeling f:X→{1,2,…,r} of X is distinguishing (with respect to Γ) if the only label preserving permutation of X in Γ is the identity. The distinguishing number, D_Γ(X), of the action of Γ on X is the minimum r for which there is an r-labeling which is distinguishing. This paper investigates the relation between the cardinality of a set X and the distinguishing numbers of group actions on X. For a positive integer n, let D(n) be the set of distinguishing numbers of transitive group actions on a set X of cardinality n, i.e., D(n)={D_Γ(X):|X|=n and Γ acts transitively on X}. We prove that . Then we consider the problem of an arbitrary fixed group Γ acting on a large set. We prove that if for any action of Γ on a set Y, for each proper normal subgroup H of Γ, D_H(Y)≤2, then there is an integer n such that for any set X with |X|≥n, for any action of Γ on X with no fixed points, D_Γ(X)≤2.     

Intersection cohomology of the circle actions

A classical result says that a free action of the circle S¹ on a topological space X is geometrically classified by the orbit space B and by a cohomological class e∈H²(B,Z), the Euler class. When the action is not free we have a difficult open question:

(Π)

“Is the space X determined by the orbit space B and the Euler class?”

The main result of this work is a step towards the understanding of the above question in the category of unfolded pseudomanifolds. We prove that the orbit space B and the Euler class determine:

•

the intersection cohomology of X,

•

the real homotopy type of X.

     

混沌群作用

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｉｓｐａｐｅｒｉｓｔｈｅｓｅｑｕｅｌｔｏ[1 ,2 ].Ｃａｉｒｎｓｅｔａｌ.[1] ｉｎｔｒｏｄｕｃｅｄｔｈｅｎｏｔｉｏｎｏｆａｃｈａｏｔｉｃｇｒｏｕｐａｃｔｉｏｎａｓａｇｅｎｅｒａｌｉｚａｔｉｏｎｏｆｃｈａｏｔｉｃｄｙｎａｍｉｃａｌｓｙｓｔｅｍｓ(ｓｅｅｄｅｆｉｎｉｔｉｏｎｂｅｌｏｗ) .Ｔｈｅｙｓｈｏｗｅｄｔｈａｔｔｈｅｃｉｒｃｌｅｄｏｅｓｎｏｔａｄｍｉｔａｃｈａｏｔｉｃａｃｔｉｏｎｏｆａｎｙｇｒｏｕｐ ,ａｎｄｃｏｎｓｔｒｕｃｔｅｄａｃｈａｏｔｉｃａｃｔｉｏｎｏｆＧ =Ｚ×…     

Enveloping actions and Takai duality for partial actions

We show that any partial action on a topological space X is the restriction of a suitable global action, called enveloping action, that is essentially unique. In the case of C∗-algebras, we prove that any partial action has a unique enveloping action up to Morita equivalence, and that the corresponding reduced crossed products are Morita equivalent. The study of the enveloping action up to Morita equivalence reveals the form that Takai duality takes for partial actions. By applying our constructions, we prove that the reduced crossed product of the reduced cross-sectional algebra of a Fell bundle by the dual coaction is liminal, postliminal, or nuclear, if and only if so is the unit fiber of the bundle. We also give a non-commutative generalization of the well-known fact that the integral curves of a vector field on a compact manifold are defined on all of .     

Stiefel-Whitney classes and toral actions

Certain Stiefel-Whitney classes of manifolds with smooth, effective toral actions are shown to be computable in terms of Poincare duals of fixed point sets of isotropy subgroups. As an application the toral degrees of symmetry of certain Dold manifolds are determined.     

The biinvariant diagonal class for Hamiltonian torus actions

Suppose that an algebraic torus G acts algebraically on a projective manifold X with generically trivial stabilizers. Then the Zariski closure of the set of pairs {(x,y)∈X×X|y=gx for some g∈G} defines a nonzero equivariant cohomology class . We give an analogue of this construction in the case where X is a compact symplectic manifold endowed with a Hamiltonian action of a torus, whose complexification plays the role of G. We also prove that the Kirwan map sends the class [ΔG] to the class of the diagonal in each symplectic quotient. This allows to define a canonical right inverse of the Kirwan map.     

Relative impatience determines preference between contract bargaining and repeated bargaining

In this paper we consider the effect of the `impatience ratio' I (of the worker discount factor to the firm discount factor) on the preferences of the players between two bargaining schemes in an asymmetric information wage bargaining context. The firm has private information about the worker's value and the worker makes wage demands. In the contact bargaining scheme, a wage demand which is accepted in one period is binding for all future periods (and hence the bargaining ends after acceptance of a wage demand). In the repeated bargaining scheme, the parties continue to bargain irrespective of whether the worker has been hired or not, and any accepted wage demand is only valid for the period in which it was accepted. We establish the following results under the assumption that the worker's value is uniformly distributed on an interval: When the firm is more patient than the worker (I<1) both parties prefer contract bargaining, and when the worker is more patient than the firm (I >1) both prefer repeated bargaining. For any value of I, the preferred type of bargaining gives the lower unemployment.  The work of Bae has already shown that when players are equally patient (I=1) the players are indifferent between the two schemes, regardless of the distribution of the worker's value. This paper shows that Bae's indifference result (Bae, 1991) cannot be extended to unequally patient players. Received: December 1996/Final version: October 1998     

On Sobolev infinitesimal rigidity of linear hyperbolic actions on the 2-torus*

Let A be a symmetric hyperbolic matrix in SL(2, ℤ) and Γ the subgroup of SL(2, ℤ) generated by A. We aim to study the infinitesimal rigidity of the standard action of Γ on the torus . More precisely, we will consider the Sobolev W^s–infinitesimal rigidity of this action (that is to determine if the cohomology space H¹(Γ,W^s (T M)) is trivial or not), and show that it is W^s–infinitesimally rigid only if 0 ≤ s < 1. A consequence will be that this action is not C^∞–infinitesimally rigid. *I would like to thank A. El Kacimi for introducing me this problem about which we had many fruitful discussions.     

关于李群胚和泊松作用的讨论

定义了纤维丛的相配群胚的概念,从作用的角度研究了李群胚与主丛的关系;给出了一个泊松群胚在泊松流形上的作用是泊松作用的充要条件;文末得到了一些关于泊松流形上Casimir函数的结果.     

Some examples of free actions on products of spheres

If G₁ and G₂ are finite groups with periodic Tate cohomology, then G₁×G₂ acts freely and smoothly on some product Sⁿ×Sⁿ.     

On maximal actions and <Emphasis Type=Italic>w</Emphasis>-maximal actions of finite hypergroups

Sunder and Wildberger (J. Algebr. Comb. 18, 135–151, 2003) introduced the notion of actions of finite hypergroups, and studied maximal irreducible actions and *-actions. One of the main results of Sunder and Wildberger states that if a finite hypergroup K admits an irreducible action which is both a maximal action and a *-action, then K arises from an association scheme. In this paper we will first show that an irreducible maximal action must be a *-action, and hence improve Sunder and Wildberger’s result (Theorem 2.9). Another important type of actions is the so-called w-maximal actions. For a w-maximal action π:K→Aff (X), we will prove that π is faithful and |X|≥|K|, and |K| is the best possible lower bound of |X|. We will also discuss the strong connectivity of the digraphs induced by a w-maximal action.     

The space of stable weak equivalence classes of measure-preserving actions

The concept of (stable) weak containment for measure-preserving actions of a countable group Γ is analogous to the classical notion of (stable) weak containment of unitary representations. If Γ is amenable then the Rokhlin lemma shows that all essentially free actions are weakly equivalent. However if Γ is non-amenable then there can be many different weak and stable weak equivalence classes. Our main result is that the set of stable weak equivalence classes naturally admits the structure of a Choquet simplex. For example, when $\mathrm{\Gamma }=\mathbb{Z}$ this simplex has only a countable set of extreme points but when Γ is a nonamenable free group, this simplex is the Poulsen simplex. We also show that when Γ contains a nonabelian free group, this simplex has uncountably many strongly ergodic essentially free extreme points.     

Unconditional integrability for dual actions

The dual action of a locally compact abelian group, in the context of C^*-algebraic bundles, is shown to satisfy an integrability property, similar to Rieffel's proper actions. The tools developed include a generalization of Bochner's integral as well as a Fourier inversion formula for operator valued maps.Partially supported by CNPq, Brazil.     

A generalization of Dirichlet approximation theorem for the affine actions on real line

In this paper, we obtain strong density results for the orbits of real numbers under the action of the semigroup generated by the affine transformations T₀(x)=x/a and T₁(x)=bx+1, where a,b>1. These density results are formulated as generalizations of the Dirichlet approximation theorem and improve the results of Bergelson, Misiurewicz, and Senti. We show that for any x,u>0 there are infinitely many elements γ in the semigroup generated by T₀ and T₁ such that |γ(x)−u|<C(t1/|γ|−1), where C and t are constants independent of γ, and |γ| is the length of γ as a word in the semigroup. Finally, we discuss the problem of approximating an arbitrary real number by the ratios of prime numbers and the ratios of logarithms of prime numbers.     

Generalized group actions in a global setting

We study generalized group actions on differentiable manifolds in the Colombeau framework, extending previous work on flows of generalized vector fields and symmetry group analysis of generalized solutions. As an application, we analyze group invariant generalized functions in this setting.     

Separating equilibria in a continuous-time bargaining model with two-sided uncertainty

In this paper, we analyze the class of all smooth separating sequential equilibria in a continuous-time bargaining model with two-sided uncertainty. Trade between players occurs whenever there is surplus to be shared and delay is used to signal their valuations. When the buyer and the seller have a common discount rate, we show that the final outcome is unique among all these equilibria: the difference between the highest possible buyer's valuation and the lowest possible seller's valuation always narrows down at a rate exactly equal to the discount rate. When their discount rates differ, the more patient side always reveals his valuation first in the unique smooth separating equilibrium. Received: November 1997/Final version: December 1999