Pareto Optimality, Game Theory and Equilibria / Edition 1by Panos M. Pardalos
Humanshavealwaysbeeninvolvedinsituationswheredecisionsmustbemade 1 that bestt the circumstances. We read, for instance, in Homer’s Iliad, the oldest written European composition (eighth century B. C. ): So he taunted. Deiphobus’ mind was torn – should he pull back and call a friend to his side, some hardy Trojan, or take the Argive on… See more details below
Humanshavealwaysbeeninvolvedinsituationswheredecisionsmustbemade 1 that bestt the circumstances. We read, for instance, in Homer’s Iliad, the oldest written European composition (eighth century B. C. ): So he taunted. Deiphobus’ mind was torn – should he pull back and call a friend to his side, some hardy Trojan, or take the Argive on alone? As he thought it out, therst way seemed the best. He went for Aeneas The decision taken may or may not a?ect and be affected by other - cision makers. The best decision may depend on one or more objectives of the decision maker. The decision may concern a static situation or a si- ation that evolves in time. Thus, mathematical and algorithmic tools have been developed in order to model, analyze, and resolve such decision-making processes. Mathematical programming, multiobjective optimization, optimal control theory, and static and dynamic game theory provide the language and the tools to achieve such goals. The notions of optimality, Pareto efficiency, and equilibrium are intimately related in a mathematical sense and tightly connected through the notions of Karush–Kuhn–Tucker (KKT) optimality, complementarity, variational inequalities, andxed points. The problem - derlying the search for an optimal point, an efficient point, an equilibrium, or axed point is essentially the same. It is true that we can recognize in ancient texts the roots for the need of such mathematical formalism.
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Table of Contents
Part I Game and Game Theory.- Minimax: Existence and Stability.- Recent Advances in Minimax Theory and Applications.- On Noncooperative Games, Minimax Theorems and Equilibrium Problems.- Nonlinear Games.- Scalar Asymptotic Contractivity and Fixed-Points for Nonexpansive Mappings on Unbounded Sets.- Cooperative Combinatorial Games.- Algorithmic Cooperative Game Theory.- A Survey of Bicooperative Game Theory.- Cost Allocation in Combinatorial Optimization Games.- Time-Dependent Equilibrium Problems.- Differential Games of Multiple Agents and Geometrical Structures.- Convexity in Differential Games.- Game Dynamic Problems for Systems with Fractional Derivatives.- Projected Dynamical Systems, Evolutionary Variational Inequalities, Applications, and a Computational Procedure.- Strategic Audit Policies Without Commitment.- Optimality and Efficiency in Auctions Design: A Survey.- Part II Multiobjective, KKT, Bilevel.- Solution Concepts and an Approximation Kuhn-Tucker Approach for Fuzzy Multi-Objective Linear Bilevel Programming.- Pareto Optimality.- Multiobjective Optimization: A Brief Overview.- Parametric Multiobjective Optimization.- Part III Applications.- The Extended Linear Complementarity Problem and Its Applications in Analysis and Control of Discrete-Event Systems.- Traffic Assignmetn: Equilibrium Models.- Investment Paradoxes in Electricity Networks.- Algorithms for Network Interdiction and Fortification Games.- Game Theoretical Approaches in Wireless Networks.- A Military Application of Viability: Winning Cones, Differential Inclusions and Lanchester Type Models for Combat.- Statics and Dynamics of Global Supply Chain Networks.- Game Theory Models and Their Applications in Inventory Management in Supply Chain.
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