Absorbing Sets in Coalitional Systems

The purpose of this paper is twofold: First, to present an approach and a solution for analyzing the stability of coalition structures: We define a coalitional system (a set and a binary relation on that set) that explains the transitions between coalition structures and we propose to solve these systems using the absorbing sets solution for abstract systems. Second, to perform an analysis of this approach to evidence its utility in determining the stable coalition structures for some socioeconomic problems. We find that the absorbing sets solution efficiently solves this class of coalitional systems.coalition structures, coalitional systems, absorbing sets solution

Internal Organization of Firms and Cartel Formation

We introduce and characterize a new solution concept for TU games. The new soluction is called SD-prenucleolus and is a lexicographic value although is not a weighted prenucleolus. The SD-prenucleolus satisfies several desirable poperties and is the only known solution that satisfies core stability, strong aggegate monotonicity and null player out property in the class of balanced games. The SD-prenucleolus is the only known solution that satisfies core stability continuity and is monotonic in the class of veto balanced games.absorbing sets solution, cartels, stability, strategic delegation

Chaotic Weak Chimeras and their Persistence in Coupled Populations of Phase Oscillators

Nontrivial collective behavior may emerge from the interactive dynamics of many oscillatory units. Chimera states are chaotic patterns of spatially localized coherent and incoherent oscillations. The recently-introduced notion of a weak chimera gives a rigorously testable characterization of chimera states for finite-dimensional phase oscillator networks. In this paper we give some persistence results for dynamically invariant sets under perturbations and apply them to coupled populations of phase oscillators with generalized coupling. In contrast to the weak chimeras with nonpositive maximal Lyapunov exponents constructed so far, we show that weak chimeras that are chaotic can exist in the limit of vanishing coupling between coupled populations of phase oscillators. We present numerical evidence that positive Lyapunov exponents can persist for a positive measure set of this inter-population coupling strength

Tensor products and regularity properties of Cuntz semigroups

The Cuntz semigroup of a C*-algebra is an important invariant in the structure and classification theory of C*-algebras. It captures more information than K-theory but is often more delicate to handle. We systematically study the lattice and category theoretic aspects of Cuntz semigroups. Given a C*-algebra $A$, its (concrete) Cuntz semigroup $Cu(A)$ is an object in the category $Cu$ of (abstract) Cuntz semigroups, as introduced by Coward, Elliott and Ivanescu. To clarify the distinction between concrete and abstract Cuntz semigroups, we will call the latter $Cu$-semigroups. We establish the existence of tensor products in the category $Cu$ and study the basic properties of this construction. We show that $Cu$ is a symmetric, monoidal category and relate $Cu(A\otimes B)$ with $Cu(A)\otimes_{Cu}Cu(B)$ for certain classes of C*-algebras. As a main tool for our approach we introduce the category $W$ of pre-completed Cuntz semigroups. We show that $Cu$ is a full, reflective subcategory of $W$. One can then easily deduce properties of $Cu$ from respective properties of $W$, e.g. the existence of tensor products and inductive limits. The advantage is that constructions in $W$ are much easier since the objects are purely algebraic. We also develop a theory of $Cu$-semirings and their semimodules. The Cuntz semigroup of a strongly self-absorbing C*-algebra has a natural product giving it the structure of a $Cu$-semiring. We give explicit characterizations of $Cu$-semimodules over such $Cu$-semirings. For instance, we show that a $Cu$-semigroup $S$ tensorially absorbs the $Cu$-semiring of the Jiang-Su algebra if and only if $S$ is almost unperforated and almost divisible, thus establishing a semigroup version of the Toms-Winter conjecture.Comment: 195 pages; revised version; several proofs streamlined; some results corrected, in particular added 5.2.3-5.2.

Characteristic Kernels and Infinitely Divisible Distributions

We connect shift-invariant characteristic kernels to infinitely divisible distributions on $\mathbb{R}^{d}$. Characteristic kernels play an important role in machine learning applications with their kernel means to distinguish any two probability measures. The contribution of this paper is two-fold. First, we show, using the L\'evy-Khintchine formula, that any shift-invariant kernel given by a bounded, continuous and symmetric probability density function (pdf) of an infinitely divisible distribution on $\mathbb{R}^d$ is characteristic. We also present some closure property of such characteristic kernels under addition, pointwise product, and convolution. Second, in developing various kernel mean algorithms, it is fundamental to compute the following values: (i) kernel mean values $m_P(x)$, $x \in \mathcal{X}$, and (ii) kernel mean RKHS inner products ${\left\langle m_P, m_Q \right\rangle_{\mathcal{H}}}$, for probability measures $P, Q$. If $P, Q$, and kernel $k$ are Gaussians, then computation (i) and (ii) results in Gaussian pdfs that is tractable. We generalize this Gaussian combination to more general cases in the class of infinitely divisible distributions. We then introduce a {\it conjugate} kernel and {\it convolution trick}, so that the above (i) and (ii) have the same pdf form, expecting tractable computation at least in some cases. As specific instances, we explore $\alpha$-stable distributions and a rich class of generalized hyperbolic distributions, where the Laplace, Cauchy and Student-t distributions are included

A noncommutative model for higher twisted K-Theory

We develop a operator algebraic model for twisted $K$-theory, which includes the most general twistings as a generalized cohomology theory (i.e. all those classified by the unit spectrum $bgl_1(KU)$). Our model is based on strongly self-absorbing $C^*$-algebras. We compare it with the known homotopy theoretic descriptions in the literature, which either use parametrized stable homotopy theory or $\infty$-categories. We derive a similar comparison of analytic twisted $K$-homology with its topological counterpart based on generalized Thom spectra. Our model also works for twisted versions of localizations of the $K$-theory spectrum, like $KU[1/n]$ or $KU_{\mathbb{Q}}$.Comment: 28 page

The Open Method of Coordination (OMC) as an Evolutionary Learning Process

We interpret the Open Method of Coordination (OMC), recently adopted by the EU as a mode of governance in the area of social policy and other fields, as an imitative learning dynamics of the type considered in evolutionary game theory. The best-practise feature and the iterative design of the OMC correspond to the behavioral rule "imitate the best." In a redistribution game with utilitarian governments and mobile welfare beneficiaries, we compare the outcomes of imitative behavior (long-run evolutionary equilibrium), decentralized best-response behavior (Nash equilibrium), and coordinated policies. The main result is that the OMC allows policy coordination on a strict subset of the set of Nash equilibria, favoring in particular coordination on intermediate values of the policy instrument

Equivariant property (SI) revisited

We revisit Matui-Sato's notion of property (SI) for C*-algebras and C*-dynamics. More specifically, we generalize the known framework to the case of C*-algebras with possibly unbounded traces. The novelty of this approach lies in the equivariant context, where none of the previous work allows one to (directly) apply such methods to actions of amenable groups on highly non-unital C*-algebras, in particular to establish equivariant Jiang-Su stability. Our main result is an extension of an observation by Sato: For any countable amenable group $\Gamma$ and any non-elementary separable simple nuclear C*-algebra $A$ with strict comparison, every $\Gamma$-action on $A$ has equivariant property (SI). A more general statement involving relative property (SI) for inclusions into ultraproducts is proved as well. As a consequence we show that if $A$ also has finitely many rays of extremal traces, then every $\Gamma$-action on $A$ is equivariantly Jiang-Su stable. We moreover provide applications of the main result to the context of strongly outer actions, such as a generalization of Nawata's classification of strongly outer automorphisms on the (stabilized) Razak-Jacelon algebra.Comment: v4 36 pages; this version has been accepted at Analysis & PD