On Solutions For N Person Games
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Author | : Harold William Kuhn |
Publisher | : Princeton University Press |
Total Pages | : 408 |
Release | : 2016-03-02 |
Genre | : Mathematics |
ISBN | : 1400881978 |
These two new collections, numbers 28 and 29 respectively in the Annals of Mathematics Studies, continue the high standard set by the earlier Annals Studies 20 and 24 by bringing together important contributions to the theories of games and of nonlinear differential equations.
Author | : WILLIAM FRANKLIN LUCAS |
Publisher | : |
Total Pages | : 108 |
Release | : 1963 |
Genre | : Games of strategy (Mathematics) |
ISBN | : |
Author | : Anatol Rapoport |
Publisher | : Courier Corporation |
Total Pages | : 337 |
Release | : 2013-06-17 |
Genre | : Mathematics |
ISBN | : 0486143678 |
DIVSequel to Two-Person Game Theory introduces necessary mathematical notation (mainly set theory), presents basic concepts and models, and provides applications to social situations. /div
Author | : Alvin E. Roth |
Publisher | : Cambridge University Press |
Total Pages | : 342 |
Release | : 1988-10-28 |
Genre | : Business & Economics |
ISBN | : 1107717213 |
Composed in honour of the sixty-fifth birthday of Lloyd Shapley, this volume makes accessible the large body of work that has grown out of Shapley's seminal 1953 paper. Each of the twenty essays concerns some aspect of the Shapley value. Three of the chapters are reprints of the 'ancestral' papers: Chapter 2 is Shapley's original 1953 paper defining the value; Chapter 3 is the 1954 paper by Shapley and Shubik applying the value to voting models; and chapter 19 is Shapley's 1969 paper defining a value for games without transferable utility. The other seventeen chapters were contributed especially for this volume. The first chapter introduces the subject and the other essays in the volume, and contains a brief account of a few of Shapley's other major contributions to game theory. The other chapters cover the reformulations, interpretations and generalizations that have been inspired by the Shapley value, and its applications to the study of coalition formulation, to the organization of large markets, to problems of cost allocation, and to the study of games in which utility is not transferable.
Author | : Harold William Kuhn |
Publisher | : Princeton University Press |
Total Pages | : 328 |
Release | : 2020-11-10 |
Genre | : Business & Economics |
ISBN | : 1400829151 |
Classics in Game Theory assembles in one sourcebook the basic contributions to the field that followed on the publication of Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern (Princeton, 1944). The theory of games, first given a rigorous formulation by von Neumann in a in 1928, is a subfield of mathematics and economics that models situations in which individuals compete and cooperate with each other. In the "heroic era" of research that began in the late 1940s, the foundations of the current theory were laid; it is these fundamental contributions that are collected in this volume. In the last fifteen years, game theory has become the dominant model in economic theory and has made significant contributions to political science, biology, and international security studies. The central role of game theory in economic theory was recognized by the award of the Nobel Memorial Prize in Economic Science in 1994 to the pioneering game theorists John C. Harsanyi, John Nash, and Reinhard Selten. The fundamental works for which they were honored are all included in this volume. Harold Kuhn, himself a major contributor to game theory for his reformulation of extensive games, has chosen eighteen essays that constitute the core of game theory as it exists today. Drawn from a variety of sources, they will be an invaluable tool for researchers in game theory and for a broad group of students of economics, political science, and biology.
Author | : Frank C. Zagare |
Publisher | : SAGE |
Total Pages | : 100 |
Release | : 1984-07 |
Genre | : Mathematics |
ISBN | : 9780803920507 |
Professor Zagare provides methods for analysing the structure of the game; considers zero and nonzero-sum games and the fundamental 'minimax theorem'; and investigates games with more than two players, including the possibility of coalitions between players.
Author | : Bernhardt Liebermann |
Publisher | : Routledge |
Total Pages | : 442 |
Release | : 2012-07-26 |
Genre | : Social Science |
ISBN | : 1136816062 |
First published in 1971, Social Choice is both a text and reference containing the proceedings of a conference dealing with contemporary work on the normative and descriptive aspects of the social choice problem. This reissue will be of interest to advanced undergraduate and graduate courses on group decision making and social choice. Economists, social psychologists, political scientists and sociologists will welcome this valuable work.
Author | : Anatol Rapoport |
Publisher | : Springer Science & Business Media |
Total Pages | : 287 |
Release | : 2012-12-06 |
Genre | : Social Science |
ISBN | : 9401021619 |
Game theory could be formally defined as a theory of rational decision in conflict situations. Models of such situations, as they are conceived in game theory, involve (1) a set of decision makers, called players; (2) a set of strategies available to each player; (3) a set of outcomes, each of which is a result of particular choices of strategies made by the players on a given play of the game; and (4) a set of payoffs accorded to each player in each of the possible outcomes. It is assumed that each player is 'individually rational', in the sense that his preference ordering of the outcomes is determined by the order of magnitudes of his (and only his) associated payoffs. Further, a player is rational in the sense that he assumes that every other player is rational in the above sense. The rational player utilizes knowledge of the other players' payoffs in guiding his choice of strategy, because it gives him information about how the other players' choices are guided. Since, in general, the orders of magnitude of the payoffs that accrue to the several players in the several outcomes do not coincide, a game of strategy is a model of a situation involving conflicts of interests.
Author | : William F. Lucas |
Publisher | : American Mathematical Soc. |
Total Pages | : 138 |
Release | : 1981-12-31 |
Genre | : Mathematics |
ISBN | : 9780821867334 |
Author | : Theo S. H. Driessen |
Publisher | : Springer Science & Business Media |
Total Pages | : 235 |
Release | : 2013-03-09 |
Genre | : Business & Economics |
ISBN | : 9401577870 |
The study of the theory of games was started in Von Neumann (1928), but the development of the theory of games was accelerated after the publication of the classical book "Theory of games and economic behavior" by Von Neumann and Morgenstern (1944). As an initial step, the theory of games aims to put situations of conflict and cooperation into mathematical models. In the second and final step, the resulting models are analysed on the basis of equitable and mathematical reasonings. The conflict and/or cooperative situation in question is generally due to the interaction between two or more individuals (players). Their interaction may lead up to several potential payoffs over which each player has his own preferences. Any player attempts to achieve his largest possible payoff, but the other players may also exert their influence on the realization of some potential payoff. As already mentioned, the theory of games consists of two parts, a modelling part and a solution part. Concerning the modelling part, the mathematical models of conflict and cooperative situations are described. The description of the models includes the rules, the strategy space of any player, potential payoffs to the players, the preferences of each player over the set of all potential payoffs, etc. According to the rules, it is either permitted or forbidden that the players communicate with one another in order to make binding agreements regarding their mutual actions.