Sequential Stability Research Articles

Interrelationships among noncooperative and coalition stability concepts

Insightful theorems are established on interrelationships among coalition and noncooperative stability concepts defined within the paradigm of the Graph Model for Conflict Resolution. More specifically, the newly defined coalition stability definitions that are considered are coalition Nash stability (CNash), coalition general metarationality (CGMR), coalition symmetric metarationality (CSMR) and coalition sequential stability (CSEQ), along with their earlier-defined noncooperative versions. A range of interesting new theorems are derived to establish connections among these coalition stability concepts as well as between noncooperative and coalition stability definitions. Applications with respect to the games of Prisoner’s Dilemma and Chicken, as well as a groundwater contamination dispute, demonstrate how the various stability definitions can be applied in practice and confirm the validity of some of the theorems as well as point out, by example, certain types of relationships which cannot hold.

Policy Equilibrium and Generalized Metarationalities for Multiple Decision-Maker Conflicts

A policy equilibrium is defined, and its properties investigated, for conflicts with more than two decision makers (DMs). A fundamental construction is the metarational tree, which expresses DMs' interactions as sequences of rounds, each consisting of an initial move by the focal DM followed by countermoves by the opponents. Using the metarational tree, the stability definitions of the graph model for conflict resolution can be adapted to apply to policies. These generalized metarational stabilities are shown to generalize Nash, general metarational, and symmetric metarational stabilities. Relationships among generalized metarationalities are derived, as are their connections with policy equilibria. Finally, the refinement that allows only credible moves (moves that are in the immediate interest of the mover) produces a new family of credible generalized metarational stabilities that generalizes the concept of sequential stability in the graph model.

Mathematical theory of compressible, viscous, and heat conducting fluids

We develop a mathematical theory of compressible, viscous, and heat conducting fluids based on the concept of weak solutions and the second law of thermodynamics. We derive suitable a priori estimates and show the weak sequential stability property for the complete Navier–Stokes–Fourier system.

Sequentially Stable Coalition Structures

In this paper, we examine the question of which coalition structures are formed in cooperative games with externalities. We introduce a stability concept for a coalition structure called a sequentially stable coalition structure by extending the concept of an equilibrium binding agreement (EBA) due to Ray and Vohra (1997). In an EBA, coalitions can only break up into smaller sizes of coalitions, but not merge into larger sizes of coalitions. On the other hand, in our concept of sequential stability, both breaking up and merging are allowed for coalitions. We also use a “step-by-step” approach to describe negotiation steps concretely by restricting how coalition structures can change: when one coalition structure is changed to another one, either (i) only one merging of two separate coalitions into a coalition occurs, or (ii) only one breaking up of a coalition into two separate coalitions happens. As an application of our stability notion, we show that the coalition structure consisting of only the grand coalition structure can be sequentially stable in common pool resource games.

Sequential Lagrangian Conditions for Convex Programs with Applications to Semidefinite Programming

In this paper it is shown that, in the absence of any regularity condition, sequential Lagrangian optimality conditions as well as a sequential duality results hold for abstract convex programs. The significance of the results is that they yield the standard optimality and duality results for convex programs under a simple closed-cone condition that is much weaker than the well-known constraint qualifications. As an application, a sequential Lagrangian duality, saddle-point conditions, and stability results are derived for convex semidefinite programs.

A regularizing effect of radiation in the equations of fluid dynamics

We investigate the properties of a class of variational solutions to the equations of fluid dynamics when radiation effects are taken into account. The main aim is to prove weak sequential stability of the solution set under certain hypotheses imposed on the pressure, viscosity, and heat conductivity. Copyright © 2004 John Wiley & Sons, Ltd.

Weak Sequential Stability of the Set of Admissible Variational Solutions to the Navier--Stokes--Fourier System

We define and investigate variational (weak) solutions of the initial-boundary-value problem for the Navier--Stokes--Fourier system with the general pressure law. We prove that the set of these solutions is weakly sequentially stable.

Strength of Preference in the Graph Model for Conflict Resolution

A new preference structure that includes a simple relative measure of strength of preference is developed and integrated into some of the stability definitions for the graph model for conflict resolution. In this triplet preference structure, a decision-maker may greatly prefer or prefer one state or scenario to another, or may be indifferent between them. Four stability definitions (solution concepts), Nash stability (R), general metarationality (GMR), symmetric metarationality (SMR), and sequential stability (SEQ), are extended to include strong and weak stabilities for the case of conflicts with two decision makers. Theorems that clarify the interrelationships of the strong and weak versions of these solution concepts are presented. The application of this new preference structure and the associated solution concepts is demonstrated in an environmental conflict model, called the Sustainable Development Conflict. This case shows that valuable strategic insights are gained when strength of preference is integrated into the stability analysis.

The determination of the stability regions and sequential transient stability analysis of integrated AC‐DC power system consisting of bipolar dc lines via the controlling unstable equilibrium points

AbstractIn this paper, a sequential transient stability analysis of an integrated AC‐DC power system consisting of bipolar MTDC is accomplished by taking into account the variation of the amplitude of the bus voltages during transient. This variation of the bus voltages is provided by the sequential AC‐DC load flow algorithm of the AC‐DC power system with respect to the active power modified at each integration step. The algorithm has two superiority. Firstly, as DC system variables are not included in Jacobian matrix the convergence time of the algorithm and necessity of computer memory is little. Secondly, both this algorithm has been developed for bipolar system and this algorithm also can be run with current controlled, voltage controlled and power controlled terminals without making any changes in proposed method. Thus, the AC‐DC transient stability analysis is accomplished considering the true value of the ratio of the reactive power absorbed from the converters to the active power transferred through DC line by the sequential approach. In the transient analysis of the system, the DC lines loads are represented as the current injections to the buses where they are connected and its effect is reflected at the internal buses in the form of additional bus power injections. The effect of these is again reflected at the internal buses in the form of additional bus power injections. Thus, the problem in constructing a valid Lyapunov function due to the transfer conductance is eliminated.

Sequential design of a decentralized control structure for power system stabilizers

In this paper, a new procedure is developed for designing power system stabilizers under the constraint of sequential stability. This constraint is an important feature of a large scale decentralized control and deals with the property of a design technique that allows the controllers to be adjusted one at a time such that the system remains stable at all times. This constraint is due to the impossibility to adjust all decentralized controllers to the power system simultaneously (due to unavoidable delays in the communication system). The procedure adopts a linearized model of the power system in the state space representation. The stabilizing signal requires the linear feedback of the local variables only. The suggested design procedure is tested on the standard New England 39-bus system.

On the Cauchy problem for Landau equation: sequential stability, global existence

We establish here a weak stability result for sequences of solutions of the Landau equation. This result relies on the compactness properties recently shown to hold for the equation, and involves a defect measure. It enables us to prove the global existence of a renormalized solution of the ``Landau equation with a defect measure''. We establish an entropy inequality for this solution, and then study its long-time behavior.

Sequential stability of regularized constrained stackelberg problems

We are concerned with constrained Stackelberg problems, corresponding to nonzero-sum non-cooperative games, in which the constraints of the leader depend on the reaction set of the follower supposed not to be a singleton, generalizing the case considered in [2,10]. In [1], existence and approximation results have been given by considering regularized problems. Here our aim is to give stability results for such regularized problems under data perturbations, generalizing those presented in [9]

Sequential stability of the constant cost dynamic lot size model-searching for monotonicity

The set of cost inputs for which an optimal solution of the dynamic lot size model remains valid is called stability region. The size of this region may be viewed as a measure of robustness of a solution. It is an expectation that the stability regions shrink with growing time horizons and that they are monotonous in this sense. In the present paper several sufficient conditions implying monotonicity will be studied. The conditions cover the existence of planning and forecast horizons and generalize the results of a previous paper in wich monotonicity results were presented for the case of ordinary planning horizons.

CO2 and CO monolayers on MgO(100) : LEED experiments and potential energy calculations

The structure of CO 2 and CO monolayers adsorbed on MgO(100) single crystal surfaces has been determined by both LEED and semi-empirical potential calculations. The CO 2 overlayer forms a commensurate (2√2×2√2)R45 o solid phase at T≤93±1 K. The CO monolayer forms a (4×2) commensurate phase at T≤40 K which is transformed into a (3×2) phase when 41 K≤T≤49 K. Above 50 K, the CO monolayer expands uniaxially toward a (n×2) phase with a progressive loss of long-range order when temperature increases. Potential calculations interpret very well the stable geometry for CO 2 and the sequential stability of the various commensurate phases for CO

Sequential stability of the constant cost dynamic lot size model

The stability region of the dynamic lot size problem understood as the set of cost parameter inputs for which an optimal solution remains valid has been studied in various papers of Vörös and the author. Recently van Hoesel and Wagelmans discussed these results and suggested some numerical improvement. Vörös provided explicity expressions for the boundaries of the cone-like regions. Now it will be studied how the stability region behaves if the time horizon is growing. The stability region will be shown to be non-monotonous, i.e. it may be shrinking, extending or shifting. At the same time there is some monotony connected with the planning horizon property of the dynamic lot size model, i.e. some monotonous behavior can be found for neighbor planning intervals.

Cooperation in conflict analysis

Definitions and procedures are presented for modeling and analyzing cooperation that can take place in a dispute. In particular, improved definitions on cooperation are given for the situation where two decision makes can cooperate with one another in a conflict consisting of two or more decision makers. To determine the equilibria or compromise resolutions when performing a stability analysis of a game involving cooperation, a sequential stability solution concept is defined. Because the definitions for modeling and analysis include both the cooperative and the noncooperative actions that decision makers can take, the definitions provide a bridge between cooperative and noncooperative game theory. Using a simple application in labor-management negotiations, the way in which the definitions can be easily applied is explained. Future research directions are suggested, including the incorporation of cooperation into an existing decision support system for carrying out conflict analysis studies.

Conflict models in graph form: Solution concepts and their interrelationships

A comprehensive approach for modeling conflicts is the recently developed graph form of conflict models. Within the flexible structure of the graph model, solution concepts including Nash stability, the various metagame techniques, the sequential stability method of Fraser and Hipel, and Stackelberg equilibrium are defined and characterized. These stability principles are compared with the limited-move and non-myopic stabilities developed previously for the graph model framework and mathematical interrelationships in this very general context are derived. As well, some steps are taken toward the development of a taxonomy of solution concepts for the graph form.

Analyzing an International Environmental Conflict Using the Graph Model

A comprehensive approach for modeling conflicts is the recently developed graph form of conflict model. The main objectives of this paper are to characterize various solution concepts using the graph model framework and to demonstrate how these developments are useful for modeling a real world dispute. The specific solution concepts formulated here for the graph model are Nash stability, metagame analysis, and the sequential stability approach of Fraser and Hipel. These solution concepts, and the limited-move and non-myopic methods developed previously, are compared and applied in this study. Finally, a complex international environmental dispute is analyzed to demonstrate the insight which decision makers can gain from studying a conflict using this methodology

Large Scale Control System Design

An overview of some recent results obtained in the area of large scale control system design is made, in which an emphasis is placed on some of the more important differences occurring between the centralized and decentralized control problem. In particular, the following topics are discussed:(i) The large scale modelling problem.(ii) The sequential stability constraint problem.(iii) The local model problem.(iv) Some characterizations of interconnected decentralized systems.A numerical example of the load and frequency control problem for a power system is included to illustrate the results.

The Sequential Stability Index and Certain Spaces of Affine Functions

The Sequential Stability Index and Certain Spaces of Affine Functions