Multicriteria Decision Making and Differential Games

1. Front Matter

   Pages i-xv

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2. Cone Convexity, Cone Extreme Points, and Nondominated Solutions in Decision Problems with Multiobjectives

   • P. L Yu

   Pages 1-59

3. Nondominated Decisions and Cone Convexity in Dynamic Multicriteria Decision Problems

   • P. L. Yu, G. Leitmann

   Pages 61-72

4. Generalization of Domination Structures and Nondominated Solutions in Multicriteria Decision Making

   • K. Bergstresser, A. Charnes, P. L. Yu

   Pages 73-83

5. Compromise Solutions, Domination Structures, and Salukvadze’s Solution

   • P. L. Yu, G. Leitmann

   Pages 85-101

6. Multiple-Objective Optimization: Proper Equality Constraints (PEC) and Maximization of Index Vectors

   • J. G. Lin

   Pages 103-128

7. Sufficient Conditions for Preference Optimality

   • W. Stadler

   Pages 129-148

8. Individual and Collective Rationality in a Dynamic Pareto Equilibrium

   • A. Haurie, M. C. Delfour

   Pages 149-161

9. A Sufficiency Condition for Coalitive Pareto-Optimal Solutions

   • W. E. Schmitendorf, G. Moriarty

   Pages 163-172

10. On the Stackelberg Strategy in Nonzero-Sum Games

    • M. Simaan, J. B. Cruz Jr.

    Pages 173-195

11. Additional Aspects of the Stackelberg Strategy in Nonzero-Sum Games

    • M. Simaan, J. B. Cruz Jr.

    Pages 197-210

12. Switching Surfaces in N-Person Differential Games

    • I. G. Sarma, U. R. Prasad

    Pages 211-232

13. Some Fundamental Qualifications of Optimal Strategies and Transition Surfaces in Differential Games

    • P. L. Yu

    Pages 233-259

14. On a Nonsingular Singular Surface of a Differential Game

    • D. J. Wilson

    Pages 261-275

15. Equilibrium Existence Results for Simple Dynamic Games

    • P. R. Kleindorfer, M. R. Sertel

    Pages 277-295

16. A Class of Trilinear Differential Games

    • S. Clemhout, H. Y. Wan Jr.

    Pages 297-302

17. Introduction to Chapters on Two-Person Decision Problems under Uncertainty

    • Y. C. Ho, F. K. Sun

    Pages 303-303

18. Value of Information in Two-Team Zero-Sum Problems

    • Y. C. Ho, F. K. Sun

    Pages 305-319

19. On the Minimax Principle and Zero-Sum Stochastic Differential Games

    • Y. C. Ho

    Pages 321-339

20. Role of Information in the Stochastic Zero-Sum Differential Game

    • F. K. Sun, Y. C. Ho

    Pages 341-351

This volume is a collection of contributions to the subject of multicriteria decision making and differential games, all of which are based wholly or in part on papers that have appeared in the Journal of Optimization Theory and Applications. The authors take this opportunity to revise, update, or enlarge upon their earlier publications. The theory of multicriteria decision making and differential games is concerned with situations in which a single decision maker is faced with a multiplicity of usually incompatible criteria, performance indices or payoffs, or in which a number of decision makers, or players, must take into account criteria each of which depends on the decisions of all the decision makers. The first six chapters are devoted to situations involving a single decision maker, or a number of decision makers in complete collaboration and thus being in effect a single decision maker. Chapters I -IV treat various topics in the theory of domination structures and nondominated decisions. Chapter V presents a discussion of efficient, or Pareto-optimal, decisions. The approach to multicriteria decision making via preference relations is explored in Chapter VI. When there is more than one decision maker, cooperation, as well as noncooperation, is possible. Chapters VII and VIII deal with the topic of coalitions in a dynamic setting, while Chapters IX and X address the situation of two unequal decision makers, a leader and a follower.

• cooperation
• optimization

• Department of Mechanical Engineering, University of California, Berkeley, USA

  George Leitmann

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