Non-Antagonistic Games

ISBN-13: 9789401088763 / Angielski / Miękka / 2011 / 376 str.

Yu B. Germeier; Anatol Rapoport

Opis

The reality around us constantly demonstrates physical and social processes in which the interests of the participants are not diametrically opposed, though they by no means always coincide. The study of such processes (interesting in itw own right) is essential for working out ways of making decisions, that is, for choosing among available parameters of the processes. If, in view of certain considerations, a participant i h 1 f 0 h' . b c ooses a va ue Xi 0 a parameter Xi' s act on can e formally described as an attempt to maximize the function f. = -llx. - x ll. For this reason any decision on the part of the i-th participant in the process can be treated (at least a posteriori) as agoal-directed act, aimed at increasing the value of some function w. (a criterion of efficiency, a payoff, a gain, etc.), wfiich generally depends on the choices of all n participants in the process. That is w = f. (x ' .., x ), i = 1, 2, .., n. 1 i n A process described in this manner, involving several participants, each pursuing different interests and constrained in his choices of parameters by the condition X E x. is called a game - a term firmly entrenched though evide tly not felicitous."

Recenzje

`Although this book is a translation of a Russian version of about 10 years ago, this book can still be recommended as an inspiration source for researchers in the field of game theory.'
Mathematical Reviews, Issue 88F.

Spis treści

I / A General Description of Models with Non-Coincident Interests.- 1. Typical Examples of Games with Non-opposed Interests.- 2. General Description of Noncooperative Games Taking into Account Mutual Information of Co-players About Their Interests.- 3. Situations, Strategies, and Players? Knowledge About Each Other?s Moves.- 4. On the Problem of Rational Choice of Strategy.- 5. Exchange of Information and Extension of the Strategy Concept.- 6. Formal Description of Compromises and Coalitions.- II / Some Principles Involved in Choosing Rational Strategies.- 7. Optimization and Averaging.- 8. The Maximin.- 9. Absolutely Optimal Strategies and Penalizing Strategies.- 10. The Best-Guaranteed Payoff Under Exchange of Information and Fixed Order of Moves.- 11. Equilibria.- 12. Advantages and Disadvantages of Coalitions.- 13. Stability of Coalitional Decisions in Repetitive Games.- III / The Guaranteed Payoff Principle in Two-Person Games.- 14. Qualitative Games.- 15. Games with Excluded Situations.- 16. Games with Fixed Order of Moves Without Excluded Situations.- 17. Exact Information About the Co-player?s Choice: Inexact Information About His Interests.- 18. Player 1 Ignorant of Player 2?s Move.- 19. The Problem of the Maximal Guaranteed Payoff and Approximation of Games.- 20. Other Cases Involving State of Knowledge Metagames.- 21. Games with Auxiliary Performance Functions.- 22. Dynamics of Two-person Games.- 23. Remarks.- IV / Some Game Models for Multiple Players.- 24. On the Theory of Three-person Games.- 25. Equilibria and Stable Collective Decisions in Repeated Games.- 26. Side Payments as Means of Control in Hierarchical Systems.