Decomposable Penalty Method for Generalized Game Problems with Joint Constraints

We consider an extension of a noncooperative game problem where players have joint binding constraints. In this case, justification of a generalized equilibrium point needs a reasonable mechanism for attaining this state. We suggest to combine a penalty method together with shares allocation of right-hand sides, which replaces the initial problem with a sequence of the usual Nash equilibrium problems together with an upper level variational inequality as a master problem. We show convergence of solutions of these auxiliary penalized problems to a solution of the initial game problem under weak coercivity conditions.Comment: 13 page

A little about models

We discuss several aspects of creation of adequate mathematical models in other sciences. In particular, many difficulties stem from great complexity of the source systems and the presence of a variety of uncertain factors. We illustrate the effect of uncertainty on the known consumer demand model. We conclude that not every uncertainty can be represented by a random variable, and that these concepts are not equivalent. We discuss also the role of different information concepts in mathematical models. We give additional illustrative examples of models of quite complex systems.Comment: 15 page

Governance structure and Operating Performance of Japanese Major Banks

近年，銀行の経営破綻が相次ぎ，金融システムの不安定性が高まっている。そのため，銀行のガバナンス構造を明らかにし，銀行経営の効率性を高めることは喫緊の課題である。ところで，非金融企業と異なり預金という特殊な負債を保有する銀行の場合，株主によるガバナンスが重要である。本稿では， 1990年から1998年をサンプル期間として，日本の大手銀行18行のパネル・データを用いて，株式所有構造の変化，株式所有構造と経営効率性および労働分配率との関係を分析した。その結果，①銀行の株式所有構造は経営効率性を重視する株主の保有比率が上昇する傾向にあること，②銀行経営に対して株主は経営効率性を高める方向で影響を与えていること，③株式保有比率が高いほど労働分配率が低下すること，すなわち株主への分配が多くなる傾向があること，の3点が明らかになった。従って，少なくとも1990年代において，銀行のガバナンス構造は株主への利益分配を重視する「新古典派型企業」としての性格を示していると言える

On quasimonotone variational inequalities

In this paper, we study variational inequalities with multivalued mappings. By employing Fan's lemma, we establish the existence result for the dual formulation of variational inequalities with semi-strictly quasimonotone mappings. We also show that similar results for quasimonotone variational inequalities do not hold

An extension of the Jacobi algorithm for the complementarity problem in the presence of multivalence

The complementarity problem is examined in the case where the basic mapping is the sum of a finite number of superpositions of a univalent off-diagonal antitone mapping and a multivalent diagonal monotone one. An extension is proposed for the Jacobi algorithm, which constructs a sequence converging to a point solution. With the use of this property, the existence of a solution to the original problem is also established. Under certain additional conditions, the minimal element in the feasible set of this problem is one of its solutions. Copyright © 2005 by MAIK "Nauka/Interperiodica"

Dual approach for a class of implicit convex optimization problems

The problem of finding a solution to a system of variational inequalities, which can be interpreted as a generalization of a convex optimization problem under arbitrary right-hand side constraint perturbations, is considered. We suggest this problem to be converted into a mixed variational inequality formulation of optimality conditions for a nonconvex and nonsmooth optimization problem. The latter problem can be solved by splitting type methods. Additional examples of applications to certain equilibrium type problems are also given. © Springer-Verlag 2004

Vector network equilibrium problems with elastic demands

We consider vector models for complex systems with spatially distributed elements which arise in communication and transportation networks. In order to describe the flow distribution within such a network, we utilize the equilibrium approach, which extends the shortest path one. Being based on this approach, we investigate several networking control problems, with taking into account many factors. As a result, general vector equilibrium problems models with complex behavior of elements are suggested. In particular, they involve elastic demand functions. Due to the presence of many factors, we utilize multicriteria models with respect to different preference relations. The corresponding problems admit efficient solution methods within optimization and equilibrium frameworks. © 2011 Springer Science+Business Media, LLC

Shares Allocation Methods for Generalized Game Problems with Joint Constraints

© 2015, Springer Science+Business Media Dordrecht.We consider an extension of a noncooperative game problem where players have joint binding constraints. We suggest a shares allocation approach, which replaces the initial problem with a sequence of Nash equilibrium problems together with an upper level set-valued variational inequality as master problem. This transformation maintains the monotonicity properties of the underlying mappings. We also show that the regularization yields a decomposable penalty method, which removes complex functions in constraints within the custom noncooperative game framework and provides the single-valued master problem with strengthened monotonicity of its cost mapping