Rationality and Extensive Form Correlated Equilibria in Stochastic Games
Author: Eilon Solan
Publisher:
Published: 2000
Total Pages: 32
ISBN-13:
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Stochastic Games and Applications
Author: Abraham Neyman
Publisher: Springer
Published: 2003-10-31
Total Pages: 0
ISBN-13: 9781402014925
DOWNLOAD EBOOKThis volume is based on lectures given at the NATO Advanced Study Institute on "Stochastic Games and Applications," which took place at Stony Brook, NY, USA, July 1999. It gives the editors great pleasure to present it on the occasion of L.S. Shapley's eightieth birthday, and on the fiftieth "birthday" of his seminal paper "Stochastic Games," with which this volume opens. We wish to thank NATO for the grant that made the Institute and this volume possible, and the Center for Game Theory in Economics of the State University of New York at Stony Brook for hosting this event. We also wish to thank the Hebrew University of Jerusalem, Israel, for providing continuing financial support, without which this project would never have been completed. In particular, we are grateful to our editorial assistant Mike Borns, whose work has been indispensable. We also would like to acknowledge the support of the Ecole Poly tech nique, Paris, and the Israel Science Foundation. March 2003 Abraham Neyman and Sylvain Sorin ix STOCHASTIC GAMES L.S. SHAPLEY University of California at Los Angeles Los Angeles, USA 1. Introduction In a stochastic game the play proceeds by steps from position to position, according to transition probabilities controlled jointly by the two players.
Stochastic and Differential Games
Author: Martino Bardi
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 388
ISBN-13: 1461215927
DOWNLOAD EBOOKThe theory of two-person, zero-sum differential games started at the be ginning of the 1960s with the works of R. Isaacs in the United States and L.S. Pontryagin and his school in the former Soviet Union. Isaacs based his work on the Dynamic Programming method. He analyzed many special cases of the partial differential equation now called Hamilton Jacobi-Isaacs-briefiy HJI-trying to solve them explicitly and synthe sizing optimal feedbacks from the solution. He began a study of singular surfaces that was continued mainly by J. Breakwell and P. Bernhard and led to the explicit solution of some low-dimensional but highly nontriv ial games; a recent survey of this theory can be found in the book by J. Lewin entitled Differential Games (Springer, 1994). Since the early stages of the theory, several authors worked on making the notion of value of a differential game precise and providing a rigorous derivation of the HJI equation, which does not have a classical solution in most cases; we mention here the works of W. Fleming, A. Friedman (see his book, Differential Games, Wiley, 1971), P.P. Varaiya, E. Roxin, R.J. Elliott and N.J. Kalton, N.N. Krasovskii, and A.I. Subbotin (see their book Po sitional Differential Games, Nauka, 1974, and Springer, 1988), and L.D. Berkovitz. A major breakthrough was the introduction in the 1980s of two new notions of generalized solution for Hamilton-Jacobi equations, namely, viscosity solutions, by M.G. Crandall and P.-L.
Quantal Response Equilibrium
Author: Jacob K. Goeree
Publisher: Princeton University Press
Published: 2016-06-28
Total Pages: 328
ISBN-13: 1400880920
DOWNLOAD EBOOKQuantal Response Equilibrium presents a stochastic theory of games that unites probabilistic choice models developed in psychology and statistics with the Nash equilibrium approach of classical game theory. Nash equilibrium assumes precise and perfect decision making in games, but human behavior is inherently stochastic and people realize that the behavior of others is not perfectly predictable. In contrast, QRE models choice behavior as probabilistic and extends classical game theory into a more realistic and useful framework with broad applications for economics, political science, management, and other social sciences. Quantal Response Equilibrium spans the range from basic theoretical foundations to examples of how the principles yield useful predictions and insights in strategic settings, including voting, bargaining, auctions, public goods provision, and more. The approach provides a natural framework for estimating the effects of behavioral factors like altruism, reciprocity, risk aversion, judgment fallacies, and impatience. New theoretical results push the frontiers of models that include heterogeneity, learning, and well-specified behavioral modifications of rational choice and rational expectations. The empirical relevance of the theory is enhanced by discussion of data from controlled laboratory experiments, along with a detailed users' guide for estimation techniques. Quantal Response Equilibrium makes pioneering game-theoretic methods and interdisciplinary applications available to a wide audience.
Stochastic Games and Related Concepts
Author: T. Parthasarathy
Publisher: Springer Nature
Published: 2020-12-08
Total Pages: 127
ISBN-13: 9811565775
DOWNLOAD EBOOKThis book discusses stochastic game theory and related concepts. Topics focused upon in the book include matrix games, finite, infinite, and undiscounted stochastic games, n-player cooperative games, minimax theorem, and more. In addition to important definitions and theorems, the book provides readers with a range of problem-solving techniques and exercises. This book is of value to graduate students and readers of probability and statistics alike.
Discrete Gambling and Stochastic Games
Author: Ashok P. Maitra
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 249
ISBN-13: 1461240026
DOWNLOAD EBOOKThe theory of probability began in the seventeenth century with attempts to calculate the odds of winning in certain games of chance. However, it was not until the middle of the twentieth century that mathematicians de veloped general techniques for maximizing the chances of beating a casino or winning against an intelligent opponent. These methods of finding op timal strategies for a player are at the heart of the modern theories of stochastic control and stochastic games. There are numerous applications to engineering and the social sciences, but the liveliest intuition still comes from gambling. The now classic work How to Gamble If You Must: Inequalities for Stochastic Processes by Dubins and Savage (1965) uses gambling termi nology and examples to develop an elegant, deep, and quite general theory of discrete-time stochastic control. A gambler "controls" the stochastic pro cess of his or her successive fortunes by choosing which games to play and what bets to make.
Optimality and Equilibria in Stochastic Games
Author: Frank Thuijsman
Publisher:
Published: 1992
Total Pages: 107
ISBN-13:
DOWNLOAD EBOOKCorrelated Equilibrium in Stochastic Games
Author: Eilon Solan
Publisher:
Published: 1998
Total Pages: 28
ISBN-13:
DOWNLOAD EBOOKEquilibrium and Rationality
Author: Paul Weirich
Publisher: Cambridge University Press
Published: 1998-01-28
Total Pages: 253
ISBN-13: 0521593522
DOWNLOAD EBOOKThis major contribution to game theory offers this conception of equilibrium in games: strategic equilibrium.
Finding Correlated Equilibria in General Sum Stochastic Games
Author: Chris Murray
Publisher:
Published: 2007
Total Pages: 19
ISBN-13:
DOWNLOAD EBOOKAbstract: "Often problems arise where multiple self-interested agents with individual goals can coordinate their actions to improve their outcomes. We model these problems as general sum stochastic games. We develop a tractable approximation algorithm for computing subgame-perfect correlated equilibria in these games. Our algorithm is an extension of standard dynamic programming methods like value iteration and Q-learning. And, it is conservative: while it is not guaranteed to find all value vectors achievable in correlated equilibrium, any policy which it does find is guaranteed to be an exact equilibrium of the stochastic game (to within limits of accuracy which depend on the number of backups and not on the approximation scheme). Our new algorithm is based on the planning algorithm of [1]. That algorithm computes subgame-perfect Nash equilibria, but assumes that it is given a set of 'punishment policies' as input. Our new algorithm requires only the description of the game, an important improvement since suitable punishment policies may be difficult to come by."
