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Book
Discrete-time optimal control and games on large intervals
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ISBN: 3319529315 3319529323 Year: 2017 Publisher: Cham : Springer International Publishing : Imprint: Springer,

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Abstract

Devoted to the structure of approximate solutions of discrete-time optimal control problems and approximate solutions of dynamic discrete-time two-player zero-sum games, this book presents results on properties of approximate solutions in an interval that is independent lengthwise, for all sufficiently large intervals. Results concerning the so-called turnpike property of optimal control problems and zero-sum games in the regions close to the endpoints of the time intervals are the main focus of this book. The description of the structure of approximate solutions on sufficiently large intervals and its stability will interest graduate students and mathematicians in optimal control and game theory, engineering, and economics. This book begins with a brief overview and moves on to analyze the structure of approximate solutions of autonomous nonconcave discrete-time optimal control Lagrange problems.Next the structures of approximate solutions of autonomous discrete-time optimal control problems that are discrete-time analogs of Bolza problems in calculus of variations are studied. The structures of approximate solutions of two-player zero-sum games are analyzed through standard convexity-concavity assumptions. Finally, turnpike properties for approximate solutions in a class of nonautonomic dynamic discrete-time games with convexity-concavity assumptions are examined.


Book
Noncooperative game theory : an introduction for engineers and computer scientists
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Year: 2017 Publisher: Princeton, NJ : Princeton University Press,

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Noncooperative Game Theory is aimed at students interested in using game theory as a design methodology for solving problems in engineering and computer science. João Hespanha shows that such design challenges can be analyzed through game theoretical perspectives that help to pinpoint each problem's essence: Who are the players? What are their goals? Will the solution to "the game" solve the original design problem? Using the fundamentals of game theory, Hespanha explores these issues and more.The use of game theory in technology design is a recent development arising from the intrinsic limitations of classical optimization-based designs. In optimization, one attempts to find values for parameters that minimize suitably defined criteria-such as monetary cost, energy consumption, or heat generated. However, in most engineering applications, there is always some uncertainty as to how the selected parameters will affect the final objective. Through a sequential and easy-to-understand discussion, Hespanha examines how to make sure that the selection leads to acceptable performance, even in the presence of uncertainty-the unforgiving variable that can wreck engineering designs. Hespanha looks at such standard topics as zero-sum, non-zero-sum, and dynamics games and includes a MATLAB guide to coding.Noncooperative Game Theory offers students a fresh way of approaching engineering and computer science applications.An introduction to game theory applications for students of engineering and computer science Materials presented sequentially and in an easy-to-understand fashionTopics explore zero-sum, non-zero-sum, and dynamics gamesMATLAB commands are included

Keywords

Noncooperative games (Mathematics) --- Game theory --- Cooperative games (Mathematics) --- MATLAB. --- Minimax Theorem. --- N-player game. --- Nash equilibrium. --- Separating Hyperplane Theorem. --- Sudoku puzzle. --- action space. --- action. --- admissible Nash equilibrium. --- advertising campaign. --- alternate play. --- average security level. --- battle of the sexes. --- behavioral policy. --- behavioral saddle-point equilibrium. --- best-response equivalent games. --- bilateral symmetric game. --- bimatrix game. --- bimatrix potential. --- chicken game. --- circuit design. --- completely mixed Nash equilibrium. --- computational complexity. --- computer science. --- congestion game. --- continuous time cost-to-go. --- continuous time differential. --- continuous time dynamic programming. --- continuous time dynamic. --- convex analysis. --- convex hull. --- decoupled game. --- design methodology. --- differential game. --- discrete time cost-to-go. --- discrete time dynamic programming. --- discrete time dynamic. --- distributed resource allocation. --- dummy game. --- dynamic game. --- engineering. --- extensive form game representation. --- feedback game. --- fictitious play. --- finite one-player. --- game theory. --- graphical method. --- hyperplane. --- identical interests. --- information structure. --- linear program. --- linear quadratic dynamic. --- minimum. --- mixed Nash equilibrium. --- mixed action space. --- mixed policy. --- mixed saddle-point equilibrium. --- mixed security policy. --- multi-stage game. --- network routing. --- non-feedback game. --- non-zero-sum. --- noncooperative game theory. --- open-loop policy. --- open-loop. --- optimization-based design. --- order interchangeability property. --- policy. --- potential game. --- probability distribution. --- pure N-player game. --- pure policy. --- recursive computation. --- regret. --- robust design. --- rock-paper-scissors. --- rope-pulling. --- saddle-point equilibrium. --- security level. --- security policy. --- simultaneous play. --- single-stage game. --- state feedback information structure. --- state-feedback policy. --- stochastic policy. --- strictly dominating policy. --- symmetry game. --- tic-tac-toe. --- tree structure. --- uncertainty. --- variable termination time. --- war of attrition. --- weakly dominating policy. --- zebra in the lake. --- zero sum dynamic. --- zero-sum matrix. --- zero-sum two-person. --- zero-sum. --- MATLAB. --- Minimax Theorem. --- N-player game. --- Nash equilibrium. --- Separating Hyperplane Theorem. --- Sudoku puzzle. --- action space. --- action. --- admissible Nash equilibrium. --- advertising campaign. --- alternate play. --- average security level. --- battle of the sexes. --- behavioral policy. --- behavioral saddle-point equilibrium. --- best-response equivalent games. --- bilateral symmetric game. --- bimatrix game. --- bimatrix potential. --- chicken game. --- circuit design. --- completely mixed Nash equilibrium. --- computational complexity. --- computer science. --- congestion game. --- continuous time cost-to-go. --- continuous time differential. --- continuous time dynamic programming. --- continuous time dynamic. --- convex analysis. --- convex hull. --- decoupled game. --- design methodology. --- differential game. --- discrete time cost-to-go. --- discrete time dynamic programming. --- discrete time dynamic. --- distributed resource allocation. --- dummy game. --- dynamic game. --- engineering. --- extensive form game representation. --- feedback game. --- fictitious play. --- finite one-player. --- game theory. --- graphical method. --- hyperplane. --- identical interests. --- information structure. --- linear program. --- linear quadratic dynamic. --- minimum. --- mixed Nash equilibrium. --- mixed action space. --- mixed policy. --- mixed saddle-point equilibrium. --- mixed security policy. --- multi-stage game. --- network routing. --- non-feedback game. --- non-zero-sum. --- noncooperative game theory. --- open-loop policy. --- open-loop. --- optimization-based design. --- order interchangeability property. --- policy. --- potential game. --- probability distribution. --- pure N-player game. --- pure policy. --- recursive computation. --- regret. --- robust design. --- rock-paper-scissors. --- rope-pulling. --- saddle-point equilibrium. --- security level. --- security policy. --- simultaneous play. --- single-stage game. --- state feedback information structure. --- state-feedback policy. --- stochastic policy. --- strictly dominating policy. --- symmetry game. --- tic-tac-toe. --- tree structure. --- uncertainty. --- variable termination time. --- war of attrition. --- weakly dominating policy. --- zebra in the lake. --- zero sum dynamic. --- zero-sum matrix. --- zero-sum two-person. --- zero-sum.

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