Note On linear consistency of anonymous values for TU-games

In the framework of values for TU-games, it is shown that a particular type of consistency, called linear consistency, together with some kind of standardness for two-person games, imply efficiency, anonymity, linearity, as well as uniqueness of the value. Among others, this uniform treatment generalizes Sobolev's axiomatization of the Shapley value. Revised version: December 2001     

Assignment games with stable core

We prove that the core of an assignment game (a two-sided matching game with transferable utility as introduced by Shapley and Shubik, 1972) is stable (i.e., it is the unique von Neumann-Morgenstern solution) if and only if there is a matching between the two types of players such that the corresponding entries in the underlying matrix are all row and column maximums. We identify other easily verifiable matrix properties and show their equivalence to various known sufficient conditions for core-stability. By these matrix characterizations we found that on the class of assignment games, largeness of the core, extendability and exactness of the game are all equivalent conditions, and strictly imply the stability of the core. In turn, convexity and subconvexity are equivalent, and strictly imply all aformentioned conditions. Final version: April 1, 2001     

Fundamental cycles of pre-imputations in non-balanced TU-games

In this paper we prove a characterization for the subclass of non-balanced T U-games. The result is stated in terms of certain class of cycles of pre-imputations. A cycle is a finite sequence of pre-imputations, where each pair of neighbouring elements are interrelated to each other through a transfer of some amount of utility from members of a certain coalition to the members of the complementary coalition, with the understanding that individual gains or losses within any coalition are proportional to the number of members of the coalition. These cycles are strongly connected with a transfer scheme designed to reach a point in the core of a T U-game provided this set is non-empty.The main result of this paper provides an alternative characterization of balanced TU-games to Shapley-Bondarevas theorem.I would like to thank A. Cali for her helpful observations, and two anonymous referees for their detailed comments and suggestions to improve substantially the presentation of the paper.     

An intersection theorem in TU cooperative game theory

We prove a theorem on the intersection of the Weber sets (Weber, 1988) of two ordered cooperative games. From this theorem several consequences are derived, the inclusion of the core in the Weber set (Weber, 1988), the fact that every convex game has a large core (Sharkey, 1982), and a discrete separation theorem (Frank, 1982). We introduce a definition of general largeness, proving that the Weber set is large for any cooperative game.Institutional support from research grants SGR2001-0029 and BEC 2002-00642 is gratefully acknowledged.     

On the reduced game property for and the axiomatization of theT-value of TU-games

Summary The τ-value is a one-point solution concept for transferable utility (TU-) games. The paper introduces a particular type of a reduced game. It is established that the τ-value possesses the reduced game property with respect to the reduced game presented. That is, there is no inconsistency in what the players of the reduced game receive-either in the original game or in the reduced game-according to the τ-value concept. In addition, the paper provides an axiomatic characterization of the τ-value in terms of the relevant reduced game property and standardness for two-person games.     

Structure of Positive Solutions of Quasilinear Elliptic Equations with Critical and Supercritical Growth

The structure of positive radial solutions to a class of quasilinear elliptic equations with critical and supercritical growth is precisely studied. A large solution and a small solution are obtained for the equations. It is shown that the large solution is unique, its asymptotic behaviour and flat core are also discussed.     

Correlated equilibria of games with many players

Let G _m,n be the class of strategic games with n players, where each player has m≥2 pure strategies. We are interested in the structure of the set of correlated equilibria of games in G _m,n when n→∞. As the number of equilibrium constraints grows slower than the number of pure strategy profiles, it might be conjectured that the set of correlated equilibria becomes large. In this paper, we show that (1) the average relative measure of the set of correlated equilibria is smaller than 2⁻ⁿ; and (2) for each 1<c<m, the solution set contains c ⁿ correlated equilibria having disjoint supports with a probability going to 1 as n grows large. The proof of the second result hinges on the following inequality: Let c ₁, …, c _l be independent and symmetric random vectors in R ^k, l≥k. Then the probability that the convex hull of c ₁, …, c _l intersects R ^k ₊ is greater than or equal to . Received: December 1998/Final version: March 2000     

Logical and algorithmic properties of stable conditional independence

The logical and algorithmic properties of stable conditional independence (CI) as an alternative structural representation of conditional independence information are investigated. We utilize recent results concerning a complete axiomatization of stable conditional independence relative to discrete probability measures to derive perfect model properties of stable conditional independence structures. We show that stable CI can be interpreted as a generalization of Markov networks and establish a connection between sets of stable CI statements and propositional formulas in conjunctive normal form. Consequently, we derive that the implication problem for stable CI is coNP-complete. Finally, we show that Boolean satisfiability (SAT) solvers can be employed to efficiently decide the implication problem and to compute concise, non-redundant representations of stable CI, even for instances involving hundreds of random variables.     

The core of a class of non-atomic games which arise in economic applications

We study the core of a non-atomic game v which is uniformly continuous with respect to the DNA-topology and continuous at the grand coalition. Such a game has a unique DNA-continuous extension on the space B ₁ of ideal sets. We show that if the extension is concave then the core of the game v is non-empty iff is homogeneous of degree one along the diagonal of B ₁. We use this result to obtain representation theorems for the core of a non-atomic game of the form v=f^μ where μ is a finite dimensional vector of measures and f is a concave function. We also apply our results to some non-atomic games which occur in economic applications. Received May 1998/Revised version September 1998     

A note on the inclusion of the kernel in the core of the bilateral assignment game

In this note we prove that the kernel of a bilateral assignment game is always included in the core. This solves an outstanding open problem for bilateral assignment games. Received January 1997/Final version June 1997     

Communication, credible improvements and the core of an economy with asymmetric information

We analyze an economy with asymmetric information and endogenize the possibilities for information transmission between members of a coalition. We then define a concept of the Core that takes into account these communication possibilities. The internal consistency of the improvements is considered and an Internally Consistent Core, which requires credibility from the improvements is introduced. Received: September 1998/revised version: June 1999     

Stochastic properties of quadrature formulas

Summary The average error of suitable quadrature formulas and the stochastic error of Monte Carlo methods are both much smaller than the worst case error in many cases. This depends, however, on the classF of functions which is considered and there are counterexamples as well.Nonlinear methods, adaptive methods, or even methods with varying cardinality are not significantly better (with respect to certain stochastic error bounds) than the simplest linear methods .     

Stable equivariant abelianization, its properties, and applications

Let G be a finite group. For a based G-space X and a Mackey functor M, a topological Mackey functor is constructed, which will be called the stable equivariant abelianization of X with coefficients in M. When X is a based G-CW complex, is shown to be an infinite loop space in the sense of G-spaces. This gives a version of the RO(G)-graded equivariant Dold-Thom theorem. Applying a variant of Elmendorf's construction, we get a model for the Eilenberg-Mac Lane spectrum HM. The proof uses a structure theorem for Mackey functors and our previous results.     

Additive stable solutions on perfect cones of cooperative games

Closed kernel systems of the coalition matrix turn out to correspond to cones of games on which the core correspondence is additive and on which the related barycentric solution is additive, stable and continuous. Different perfect cones corresponding to closed kernel systems are described. Received: December 2001/Revised: July 2002 RID="*" ID="*"  This note contains the new results, which were presented by the first author in an invited lecture at the XIV Italian Meeting on Game Theory and Applications in Ischia, July 2001. The lecture was dedicated to Irinel Dragan on the occasion of his seventieth birthday.     

The term structure of interest rates in the economic and monetary union

The main purpose of this article is to present a new numerical procedure that can be used to implement a variety of different interest rate models. The new approach allows to construct no-arbitrage models for the term structure, where the stochastic process driving the rates is infinitely divisible, as in the cases of pure-diffusion and jump-diffusion mean reverting models. The new method determines a unique fully specified hexanomial tree, consistent with risk neutral probabilities. A simple forward recursive procedure solves for the entire tree. The proposed lattice model, which generalized the Hull and White [37] single-factor model, is relatively simple, computational efficient and can fit any initial term structure observed in the market. Numerical experiments demonstrate how the jump-diffusion mean reverting model is particularly suited to describe the European money market rates behavior. Interest rates controlled by the monetary authorities behave as if they are jump processes and the term structure, at short maturity, is contingent upon the levels of these official rates.     

Stable modeling in energy risk management

High price volatility in energy markets compels the companies to adopt and implement policies for measurement and management of the energy risk. A popular measure of risk exposure is the Value at Risk (VaR). Traditional methods of estimation of VaR used by major energy companies fail to capture the heavy tails and asymmetry of energy returns distributions. We suggest the use of stable distributions for modeling energy return distributions. The results of our study demonstrate that stable modeling captures asymmetry and heavy-tails of returns, and, therefore, provides more accurate estimates of energy VaR.