ON SOME PROPERTIES OF SUPERPOSITION OF OPTIMALITY PRINCIPLES FOR COOPERATIVE GAMES

2000 ◽  
Vol 02 (01) ◽  
pp. 107-116 ◽  
Author(s):  
SERGEI V. CHISTYAKOV ◽  
SVETLANA Y. MIKHAJLOVA
Keyword(s):  
Cooperative Games ◽  
Sufficient Conditions ◽  
Optimality Principle ◽  
Optimality Principles

The aim of this paper is to study the properties of superposition of optimality principles depending on the properties of optimality principles, which it is formed from. Some sufficient conditions for quasiperfectness of superposition of two optimality principles are found. It is shown, in particular, that superposition of any optimality principle like min-max principle with any monotone and continuous optimality principle is a quasiperfect optimality principle.

Some Sufficiency Conditions for Pareto-Optimal Control

1973 ◽  
Vol 95 (4) ◽  
pp. 356-361 ◽  
Author(s):  
G. Leitmann ◽  
W. Schmitendorf
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Pareto Optimality ◽  
Optimal Control Theory ◽  
Cooperative Games ◽  
Sufficient Conditions ◽  
Pareto Optimal ◽  
Vector Valued ◽  
Sufficiency Conditions

We consider the optimal control problem with vector-valued criterion (including cooperative games) and seek Pareto-optimal (noninferior) solutions. Scalarization results, together with modified sufficiency theorems from optimal control theory, are used to deduce sufficient conditions for Pareto-optimality. The utilization of these conditions is illustrated by various examples.

On Some Properties of Superposition of Optimality Principles for Cooperative Games

2000 ◽  
Vol 33 (16) ◽  
pp. 539-542
Author(s):  
Sergei V. Chistyakov ◽  
Svetlana Yu. Mikhajlova
Keyword(s):  
Cooperative Games ◽  
Optimality Principles

scholarly journals The core and superdifferential of a fuzzy TU-cooperative game

2020 ◽  
Vol 12 (2) ◽  
pp. 20-35
Author(s):  
Валерий Александрович Васильев ◽  
Valery Vasil'ev
Keyword(s):  
Cooperative Game ◽  
Cooperative Games ◽  
Sufficient Conditions ◽  
Subdifferential Calculus ◽  
The Core ◽  
Side Payments ◽  
Weak Homogeneity ◽  
Fuzzy Game

In the paper, we consider conditions providing coincidence of the cores and superdifferentials of fuzzy cooperative games with side payments. It turned out that one of the most simple sufficient conditions consists of weak homogeneity. Moreover, by applying so-called S*-representation of a fuzzy game introduced by the author, we show that for any vwith nonempty core C(v) there exists some game u such that C(v) coincides with the superdifferential of u. By applying subdifferential calculus we describe a structure of the core forboth classic fuzzy extensions of the ordinary cooperative game (e.g., Aubin and Owen extensions) and for some new continuations, like Harsanyi extensions and generalized Airport game.

scholarly journals CONVEXITY IN STOCHASTIC COOPERATIVE SITUATIONS

2005 ◽  
Vol 07 (01) ◽  
pp. 25-42 ◽  
Author(s):  
JUDITH TIMMER ◽  
PETER BORM ◽  
STEF TIJS
Keyword(s):  
Shapley Value ◽  
Cooperative Games ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Convex Game ◽  
Tu Games ◽  
New Model ◽  
The Core ◽  
Random Payoffs ◽  
Marginal Vectors

This paper introduces a new model concerning cooperative situations in which the payoffs are modeled by random variables. We analyze these situations by means of cooperative games with random payoffs. Special attention is paid to three types of convexity, namely coalitional-merge, individual-merge and marginal convexity. The relations between these types are studied and in particular, as opposed to their deterministic counterparts for TU games, we show that these three types of convexity are not equivalent. However, all types imply that the core of the game is nonempty. Sufficient conditions on the preferences are derived such that the Shapley value, defined as the average of the marginal vectors, is an element of the core of a convex game.

NULL PLAYERS OUT? LINEAR VALUES FOR GAMES WITH VARIABLE SUPPORTS

1999 ◽  
Vol 01 (03n04) ◽  
pp. 301-314 ◽  
Author(s):  
JEAN J. M. DERKS ◽  
HANS H. HALLER
Keyword(s):  
Cooperative Games ◽  
Symmetry Property ◽  
Sufficient Conditions ◽  
Function Form ◽  
Individual Values ◽  
Null Player ◽  
Main Emphasis ◽  
Weak Symmetry ◽  
Necessary And Sufficient ◽  
Characteristic Function Form

The paper studies the consequences of the Null Player Out (NPO) property for single-valued solutions on the class of cooperative games in characteristic function form. We allow for variable player populations (supports or carriers). A solution satisfies the NPO property, if elimination of a null player does not affect the payoffs of the other players. Our main emphasis lies on individual values. For linear values satisfying the null player property and a weak symmetry property, necessary and sufficient conditions for the NPO property are derived.

scholarly journals CORE CONCEPTS FOR DYNAMIC TU GAMES

2005 ◽  
Vol 07 (01) ◽  
pp. 43-61 ◽  
Author(s):  
LAURENCE KRANICH ◽  
ANDRÉS PEREA ◽  
HANS PETERS
Keyword(s):  
Cooperative Games ◽  
Sufficient Conditions ◽  
Finite Sequence ◽  
Essential Difference ◽  
Tu Games ◽  
The Core ◽  
Dynamic Setting ◽  
Core Concepts ◽  
Provided Examples

This paper is concerned with the question of how to define the core when cooperation takes place in a dynamic setting. The focus is on dynamic cooperative games in which the players face a finite sequence of exogenously specified TU-games. Three different core concepts are presented: the classical core, the strong sequential core and the weak sequential core. The differences between the concepts arise from different interpretations of profitable deviations by coalitions. Sufficient conditions are given for nonemptiness of the classical core in general and of the weak sequential core for the case of two players. Simplifying characterizations of the weak and strong sequential core are provided. Examples highlight the essential difference between these core concepts.

scholarly journals A Dynamic Optimality Principle for Water Use Strategies Explains Isohydric to Anisohydric Plant Responses to Drought

2019 ◽  
Author(s):  
Assaad Mrad ◽  
Sanna Sevanto ◽  
Jean-Christophe Domec ◽  
Yanlan Liu ◽  
Mazen Nakad ◽  
...  
Keyword(s):  
Water Use ◽  
Plant Responses ◽  
Mechanistic Models ◽  
Soil Processes ◽  
Stomatal Response ◽  
Optimality Principle ◽  
Whole Plant ◽  
Different Types ◽  
Water Use Strategy ◽  
Optimality Principles

Optimality principles that underlie models of stomatal kinetics require identifying and formulating the gain and the costs involved in opening stomata. While the gain has been linked to larger carbon acquisition, there is still debate as to the costs that limit stomatal opening. This work presents an Euler-Lagrange framework that accommodates water use strategy and various costs through the formulation of constraints. The reduction in plant hydraulic conductance due to cavitation is added as a new constraint above and beyond the hydrological balance and analyzed for three different types of whole-plant vulnerability curves. Model results show that differences in vulnerability curves alone lead to relatively iso- and aniso-hydric stomatal behavior. Moreover, this framework explains how the presence of competition (biotic or abiotic) for water alters stomatal response to declining soil water content. This contribution corroborates previous research that predicts that a plant's environment (e.g., competition, soil processes) significantly affects its response to drought and supplies the required mathematical machinery to represent this complexity. The method adopted here disentangles cause and effect of the opening and closure of stomata and complements recent mechanistic models of stomatal response to drought.

Optimum Bifurcating-Tube Tree for Gas Transport

2005 ◽  
Vol 127 (3) ◽  
pp. 550-553 ◽  
Author(s):  
Tianshu Liu
Keyword(s):  
Diffusion Zone ◽  
Convection Zone ◽  
Gas Transport ◽  
Mass Transfer Rate ◽  
Length Distribution ◽  
Diameter Distribution ◽  
Optimality Principle ◽  
Optimality Principles ◽  
Diffusion Mass ◽  
And Diffusion

This paper describes optimality principles for the design of an engineering bifurcating-tube tree consisting of the convection and diffusion zones to attain the most effective gas transport. An optimality principle is formulated for the diffusion zone to maximize the total diffusion mass-transfer rate of gas across tube walls under a constant total-volume constraint. This optimality principle produces a new diameter distribution for the diffusion zone in contrast to the classical distribution for the convection zone. In addition. this paper gives a length distribution for an engineering tree based on an optimality principle for minimizing the total weight of the tree under constraints of a finite surface and elastic criteria for structural stability. Furthermore, the optimum branching angles are evaluated based on local optimality principles for a single bifurcating-tube branch.

MULTISTAGE COOPERATIVE GAMES AND PROBLEM OF TIME CONSISTENCY

2004 ◽  
Vol 06 (01) ◽  
pp. 157-170 ◽  
Author(s):  
VICTOR ZAKHAROV ◽  
MARIA DEMENTIEVA
Keyword(s):  
Cooperative Game ◽  
Cooperative Games ◽  
Sufficient Conditions ◽  
Time Consistency ◽  
Necessary And Sufficient Conditions ◽  
Dynamic Consistency ◽  
Problem Of Time ◽  
Reduced Game ◽  
Necessary And Sufficient

In this paper we consider the problem of time-consistency of the subcore in a multistage TU-cooperative game. We propose necessary and sufficient conditions for the time-consistency of an imputation from the subcore. Based on these conditions, we suggest an algorithm providing time-consistency of a selector of the subcore. Besides, we prove consistency of the subcore with respect to the MDM-reduction. Finally we introduce the notions of reduced game and dynamic consistency for multistage cooperative games. One of the main results of this paper is a theorem stating some properties of dynamic consistency of the subcore selectors. We focus particularly on the conditions of the dynamic consistency of the subcore with respect to the MDM-reduced game.

Some Contributions to the Theory of Near-Critical Bisexual Branching Processes

2007 ◽  
Vol 44 (02) ◽  
pp. 492-505
Author(s):  
M. Molina ◽  
M. Mota ◽  
A. Ramos
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Positive Probability ◽  
Limit Laws ◽  
Bisexual Branching Processes ◽  
Probabilistic Evolution

We investigate the probabilistic evolution of a near-critical bisexual branching process with mating depending on the number of couples in the population. We determine sufficient conditions which guarantee either the almost sure extinction of such a process or its survival with positive probability. We also establish some limiting results concerning the sequences of couples, females, and males, suitably normalized. In particular, gamma, normal, and degenerate distributions are proved to be limit laws. The results also hold for bisexual Bienaymé–Galton–Watson processes, and can be adapted to other classes of near-critical bisexual branching processes.

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