A noncooperative approach to bankruptcy problems with an endogenous estate

We introduce a new class of bankruptcy problems in which the value of the estate is endogenous and depends on agents’ investment decisions. There are two investment alternatives: investing in a company (risky asset) and depositing money into a savings account (risk-free asset). Bankruptcy is possible only for the risky asset. We define a game between agents each of which aims to maximize his expected payoff by choosing an investment alternative and a company management which aims to maximize profits by choosing a bankruptcy rule. Our agents are differentiated by their incomes. We consider three most prominent bankruptcy rules in our base model: the proportional rule, the constrained equal awards rule and the constrained equal losses rule. We show that only the proportional rule is a part of any pure strategy subgame perfect Nash equilibrium. This result is robust to changes in income distribution in the economy and can be extended to a larger set of bankruptcy rules and multiple types. However, extension to multiple company framework with competition leads to equilibria where the noncooperative support for the proportional rule disappears.     

A core approach to the 0–1 equality knapsack problem

For the 0–1 knapsack problem with equality constraint a partitioning procedure is introduced which focuses on the core of the problem. The purpose of the procedure is to reduce the required preliminary sorting for large problem instances. Computational results are presented for an improved heuristic as well as for a complete (exact) algorithm showing the success of the core approach. Test problems of size up to 15–000 objects are solved within 400–ms on a standard personal computer, that is, within the time that is needed for sorting the profit-weight ratios. The core algorithm reduces the solution times by a factor of up to four for large problem instances.     

The core cover in relation to the nucleolus and the Weber set

The class of games for which the core coincides with the core cover (compromise stable games) is characterized. Moreover, an easy explicit formula for the nucleolus of this class of games is developed, using an approach based on bankruptcy problems. Also, the class of convex and compromise stable games is characterized. The relation between the core cover and the Weber set is studied and it is proved that under a weak condition their intersection is nonempty.     

Directional approach to gradual cover: the continuous case

Computational Management Science - The objective of the cover location models is covering demand by facilities within a given distance. The gradual (or partial) cover replaces abrupt drop from full...     

A new approach to the core and Weber set of multichoice games

Multichoice games have been introduced by Hsiao and Raghavan as a generalization of classical cooperative games. An important notion in cooperative game theory is the core of the game, as it contains the rational imputations for players. We propose two definitions for the core of a multichoice game, the first one is called the precore and is a direct generalization of the classical definition. We show that the precore coincides with the definition proposed by Faigle, and that the set of imputations may be unbounded, which makes its application questionable. A second definition is proposed, imposing normalization at each level, causing the core to be a convex compact set. We study its properties, introducing balancedness and marginal worth vectors, and defining the Weber set and the pre-Weber set. We show that the classical properties of inclusion of the (pre)core into the (pre)-Weber set as well as their coincidence in the convex case remain valid. A last section makes a comparison with the core defined by Van den Nouweland et al. A preliminary and short version of this paper has been presented at 4th Logic, Game Theory and Social Choice meeting, Caen, France, June 2005 (Xie and Grabisch 2005).     

Directional approach to gradual cover: a maximin objective

The objective of original cover location models is to cover demand within a given distance by facilities. Locating a given number of facilities to cover as much demand as possible is referred to as max-cover, and finding the minimum number of facilities required to cover all the demand is referred to as set covering. When the objective is to maximize the minimum cover of demand points, the maximin objective is equivalent to set covering because each demand point is either covered or not. The gradual (or partial) cover replaces abrupt drop from full cover to no cover by defining gradual decline in cover. Both maximizing total cover and maximizing the minimum cover are useful objectives using the gradual cover measure. In this paper we use a recently proposed rule for calculating the joint cover of a demand point by several facilities termed “directional gradual cover”. The objective is to maximize the minimum cover of demand points. The solution approaches were extensively tested on a case study of covering Orange County, California.

     

A coalitional procedure leading to a family of bankruptcy rules

We provide a general coalitional procedure that characterizes a family of rules for bankruptcy problems inspired by the Talmud.     

A hybridized tabu search approach for the minimum weight vertex cover problem

The minimum weight vertex cover problem is a basic combinatorial optimization problem defined as follows. Given an undirected graph and positive weights for all vertices the objective is to determine a subset of the vertices which covers all edges such that the sum of the related cost values is minimized. In this paper we apply a modified reactive tabu search approach for solving the problem. While the initial concept of reactive tabu search involves a random walk we propose to replace this random walk by a controlled simulated annealing. Numerical results are presented outperforming previous metaheuristic approaches in most cases.     

A coupled multi-component approach for bacterial methane oxidation in landfill cover layers

Methane (CH₄), which has a 25 times higher global warming potential than carbon dioxide (CO₂), can be oxidated by methanotrophic bacteria into carbon dioxide and water. The biological oxidation of methane can be considered in the passive aftercare phase of landfills in order to reduce climate-damaging methane emissions. Methanotrophic bacteria are situated within the landfill cover layer and convert the harmful methane emissions arising from the degradation of organic waste to the less harmful carbon dioxide. Hence, the passive aftercare of landfills in terms of methane oxidation layers is an efficient method to reduce contributions to the greenhouse effect. To model the coupled processes during phase transition from methane to carbon dioxide, the well-known Theory of Porous Media (TPM) combined with the Mixture Theory has been used in order to develop a multi-component Finite Element calculation concept, see [1, 3]. The thermodynamic consistent model analyzes the relevant gas productions of methane, carbon dioxide and oxygen. The model also accounts for the driving phenomena of production, diffusion and advection. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Integer solutions to bankruptcy problems with non-integer claims

In this paper, we consider a bankruptcy problem with the additional constraint that the estate has to be assigned in integer unities; differently from the approaches by other authors, we allow for non-integer claims. This situation poses new questions on the existence and the uniqueness of the solution. We propose a new solution method that leads to the “box solution”, for which uniqueness may be guaranteed introducing a ranking on the claimants. Some examples complete the paper.     

A threshold for the size of random caps to cover a sphere

Consider a unit sphere on which are placed N random spherical caps of area 4p(N). We prove that if % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% qGSbGaaeyAaiaab2gaaaWaaeWaaeaacaWGWbWaaeWaaeaacaWGobaa% caGLOaGaayzkaaGaai4Taiaad6eacaGGVaGaaeiBaiaab+gacaqGNb% Gaaeiiaiaad6eaaiaawIcacaGLPaaacqGH8aapcaaIXaaaaa!454E!\[\overline {{\rm{lim}}} \left( {p\left( N \right)\cdotN/{\rm{log }}N} \right) < 1\], then the probability that the sphere is completely covered by N caps tends to 0 as N , and if % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaWaaaeaaca% qGSbGaaeyAaiaab2gaaaWaaeWaaeaacaWGWbWaaeWaaeaacaWGobaa% caGLOaGaayzkaaGaai4Taiaad6eacaGGVaGaaeiBaiaab+gacaqGNb% Gaaeiiaiaad6eaaiaawIcacaGLPaaacqGH+aGpcaaIXaaaaa!4551!\[\underline {{\rm{lim}}} \left( {p\left( N \right)\cdotN/{\rm{log }}N} \right) > 1\], then for any integer n>0 the probability that each point of the sphere is covered more than n times tends to 1 as N .     

A note on the core

This note studies an exchange economy in which there are n traders and n “kinds” of commodities. Each trader has n utility functions corresponding to n “kinds” of commodities, respectively. Thus, a multiple non-transferable utility game can be derived from this exchange economy. It is shown that a sufficient condition for non-emptiness of the core of a multiple non-transferable utility game. The result is an extension of Scarf-Billera theorem.     

Assessing financial distress where bankruptcy is not an option: An alternative approach for local municipalities

The goal of this paper is to build an operational model for evaluating the financial viability of local municipalities in Greece. For this purpose, a multicriteria methodology is implemented combining a simulation analysis approach (stochastic multicriteria acceptability analysis) with a disaggregation technique. In particular, an evaluation model is developed on the basis of accrual financial data from 360 Greek municipalities for 2007. A set of customized to the local government context financial ratios is defined that rate municipalities and distinguish those with good financial condition from those experiencing financial problems. The model’s results are analyzed on the 2007 data as well as on a subsample of 100 local governments in 2009. The model succeeded in correctly classifying distressed municipalities according to a benchmark set by the central government in 2010. Such a model and methodology could be particularly useful for performance assessment in the context of several European Union countries that have a similar local government framework to the Greek one and apply accrual accounting techniques.     

A polyhedral approach to the alldifferent system

This paper examines the facial structure of the convex hull of integer vectors satisfying a system of alldifferent predicates, also called an alldifferent system. The underlying analysis is based on a property, called inclusion, pertinent to such a system. For the alldifferent systems for which this property holds, we present two families of facet-defining inequalities, establish that they completely describe the convex hull and show that they can be separated in polynomial time. Consequently, the inclusion property characterises a group of alldifferent systems for which the linear optimization problem (i.e. the problem of optimizing a linear function over that system) can be solved in polynomial time. Furthermore, we establish that, for systems with three predicates, the inclusion property is also a necessary condition for the convex hull to be described by those two families of inequalities. For the alldifferent systems that do not possess that property, we establish another family of facet-defining inequalities and an accompanied polynomial-time separation algorithm. All the separation algorithms are incorporated within a cutting-plane scheme and computational experience on a set of randomly generated instances is reported. In concluding, we show that the pertinence of the inclusion property can be decided in polynomial time.     

A viability approach to the skorohod problem

The theory of stochastic differential equations with reflecting boundary conditions leads to the "Skorohod" problem. Thispaper proposes a solution to this problem using techniques from viability theory and non-smooth analysis, allowing very general situations to occur.     

A random approach to the Lebesgue integral

We construct an integral of a measurable real function using randomly chosen Riemann sums and show that it converges in probability to the Lebesgue integral where this exists. We then prove some conditions for the almost sure convergence of this integral.     

A fuzzy approach to the transportation problem

The transportation problem with fuzzy supply values of the deliverers and with fuzzy demand values of the receivers is analysed. For the solution of the problem the technique of parametric programming is used. This makes it possible to obtain not only the maximizing solution (according to the Bellman-Zadeh criterion) but also other alternatives close to the optimal solution.     

A categorical approach to the maximum theorem

Berge's maximum theorem gives conditions ensuring the continuity of an optimised function as a parameter changes. In this paper we state and prove the maximum theorem in terms of the theory of monoidal topology and the theory of double categories.This approach allows us to generalise (the main assertion of) the maximum theorem, which is classically stated for topological spaces, to pseudotopological spaces and pretopological spaces, as well as to closure spaces, approach spaces and probabilistic approach spaces, amongst others. As a part of this we prove a generalisation of the extreme value theorem.