Stochastic games provide a versatile model for reactive systems that are affected by random events. This dissertation advances the algorithmic theory of stochastic games to incorporate multiple players, whose objectives are not necessarily conflicting. The basis of this work is a comprehensive complexity-theoretic analysis of the standard game-theoretic solution concepts in the context of stochastic games over a finite state space. One main result is that the constrained existence of a Nash equilibrium becomes undecidable in this setting. This impossibility result is accompanied by several positive results, including efficient algorithms for natural special cases.
This 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.
This 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.
Dynamic game theory serves the purpose of including strategic interaction in decision making and is therefore often applied to economic problems. This book presents the state-of-the-art and directions for future research in dynamic game theory related to economics. It was initiated by contributors to the 12th Viennese Workshop on Optimal Control, Dynamic Games and Nonlinear Dynamics and combines a selection of papers from the workshop with invited papers of high quality.
This book constitutes the refereed proceedings of the 20th International Symposium on Algorithms and Computation, ISAAC 2009, held in Honolulu, Hawaii, USA in December 2009. The 120 revised full papers presented were carefully reviewed and selected from 279 submissions for inclusion in the book. This volume contains topics such as algorithms and data structures, approximation algorithms, combinatorial optimization, computational biology, computational complexity, computational geometry, cryptography, experimental algorithm methodologies, graph drawing and graph algorithms, internet algorithms, online algorithms, parallel and distributed algorithms, quantum computing and randomized algorithms.
A critical challenge in deep learning is the vulnerability of deep learning networks to security attacks from intelligent cyber adversaries. Even innocuous perturbations to the training data can be used to manipulate the behaviour of deep networks in unintended ways. In this book, we review the latest developments in adversarial attack technologies in computer vision; natural language processing; and cybersecurity with regard to multidimensional, textual and image data, sequence data, and temporal data. In turn, we assess the robustness properties of deep learning networks to produce a taxonomy of adversarial examples that characterises the security of learning systems using game theoretical adversarial deep learning algorithms. The state-of-the-art in adversarial perturbation-based privacy protection mechanisms is also reviewed. We propose new adversary types for game theoretical objectives in non-stationary computational learning environments. Proper quantification of the hypothesis set in the decision problems of our research leads to various functional problems, oracular problems, sampling tasks, and optimization problems. We also address the defence mechanisms currently available for deep learning models deployed in real-world environments. The learning theories used in these defence mechanisms concern data representations, feature manipulations, misclassifications costs, sensitivity landscapes, distributional robustness, and complexity classes of the adversarial deep learning algorithms and their applications. In closing, we propose future research directions in adversarial deep learning applications for resilient learning system design and review formalized learning assumptions concerning the attack surfaces and robustness characteristics of artificial intelligence applications so as to deconstruct the contemporary adversarial deep learning designs. Given its scope, the book will be of interest to Adversarial Machine Learning practitioners and Adversarial Artificial Intelligence researchers whose work involves the design and application of Adversarial Deep Learning.
This book gives a concise presentation of the mathematical foundations of Game Theory, with an emphasis on strategic analysis linked to information and dynamics. It is largely self-contained, with all of the key tools and concepts defined in the text. Combining the basics of Game Theory, such as value existence theorems in zero-sum games and equilibrium existence theorems for non-zero-sum games, with a selection of important and more recent topics such as the equilibrium manifold and learning dynamics, the book quickly takes the reader close to the state of the art. Applications to economics, biology, and learning are included, and the exercises, which often contain noteworthy results, provide an important complement to the text. Based on lectures given in Paris over several years, this textbook will be useful for rigorous, up-to-date courses on the subject. Apart from an interest in strategic thinking and a taste for mathematical formalism, the only prerequisite for reading the book is a solid knowledge of mathematics at the undergraduate level, including basic analysis, linear algebra, and probability.
This book constitutes the proceedings of the 14th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2010, held in Lausanne, Switzerland in June 2010. The 34 papers presented were carefully reviewed and selected from 135 submissions. The conference has become the main forum for recent results in integer programming and combinatorial optimization in the non-symposium years.
A new group of contributions to the development of this theory by leading experts in the field. The contributors include L. D. Berkovitz, L. E. Dubins, H. Everett, W. H. Fleming, D. Gale, D. Gillette, S. Karlin, J. G. Kemeny, R. Restrepo, H. E. Scarf, M. Sion, G. L. Thompson, P. Wolfe, and others.
