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Game Theory & Modeling

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Exploring Language with Game Theory

In Meaningful Games, Robin Clark explains in an accessible manner the usefulness of game theory in thinking about a wide range of issues in linguistics. Clark argues that we use grammar strategically to signal our intended meanings: our choices as speaker are conditioned by what choices the hearer will make interpreting what we say. Game theory--according to which the outcome of a decision depends on the choices of others--provides a formal system that allows us to develop theories about the kind of decision making that is crucial to understanding linguistic behavior.
Clark argues the only way to understand meaning is to grapple with its social nature--that it is the social that gives content to our mental lives. Game theory gives us a framework for working out these ideas. The resulting theory of use will allow us to account for many aspects of linguistic meaning, and the grammar itself can be simplified. The results are nevertheless precise and subject to empirical testing.
Meaningful Games offers an engaging and accessible introduction to game theory and the study of linguistic meaning. No knowledge of mathematics beyond simple algebra is required; formal definitions appear in special boxes outside the main text. The book includes an extended argument in favor of the social basis of meaning; a brief introduction to game theory, with a focus on coordination games and cooperation; discussions of common knowledge and games of partial information; models of games for pronouns and politeness; and the development of a system of social coordination of reference.

This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of optimal control theory for deterministic continuous-time systems in economics. The theory of ordinary differential equations (ODEs) is the backbone of the theory developed in the book, and chapter 2 offers a detailed review of basic concepts in the theory of ODEs, including the solution of systems of linear ODEs, state-space analysis, potential functions, and stability analysis. Following this, the book covers the main results of optimal control theory, in particular necessary and sufficient optimality conditions; game theory, with an emphasis on differential games; and the application of control-theoretic concepts to the design of economic mechanisms. Appendixes provide a mathematical review and full solutions to all end-of-chapter problems.

The material is presented at three levels: single-person decision making; games, in which a group of decision makers interact strategically; and mechanism design, which is concerned with a designer's creation of an environment in which players interact to maximize the designer's objective.
The book focuses on applications; the problems are an integral part of the text. It is intended for use as a textbook or reference for graduate students, teachers, and researchers interested in applications of control theory beyond its classical use in economic growth. The book will also appeal to readers interested in a modeling approach to certain practical problems involving dynamic continuous-time models.

This text offers a systematic, rigorous, and unified presentation of evolutionary game theory, covering the core developments of the theory from its inception in biology in the 1970s through recent advances. Evolutionary game theory, which studies the behavior of large populations of strategically interacting agents, is used by economists to make predictions in settings where traditional assumptions about agents’ rationality and knowledge may not be justified. Recently, computer scientists, transportation scientists, engineers, and control theorists have also turned to evolutionary game theory, seeking tools for modeling dynamics in multiagent systems. Population Games and Evolutionary Dynamics provides a point of entry into the field for researchers and students in all of these disciplines. The text first considers population games, which provide a simple, powerful model for studying strategic interactions among large numbers of anonymous agents. It then studies the dynamics of behavior in these games.By introducing a general model of myopic strategy revision by individual agents, the text provides foundations for two distinct approaches to aggregate behavior dynamics: the deterministic approach, based on differential equations, and the stochastic approach, based on Markov processes. Key results on local stability, global convergence, stochastic stability, and nonconvergence are developed in detail. Ten substantial appendixes present the mathematical tools needed to work in evolutionary game theory, offering a practical introduction to the methods of dynamic modeling. Accompanying the text are more than 200 color illustrations of the mathematics and theoretical results; many were created using the Dynamo software suite, which is freely available on the author’s Web site. Readers are encouraged to use Dynamo to run quick numerical experiments and to create publishable figures for their own research.

A Primer, 2nd Edition

The theory of contracts grew out of the failure of the general equilibrium model to account for the strategic interactions among agents that arise from informational asymmetries. This popular text, revised and updated throughout for the second edition, serves as a concise and rigorous introduction to the theory of contracts for graduate students and professional economists. The book presents the main models of the theory of contracts, particularly the basic models of adverse selection, signaling, and moral hazard. It emphasizes the methods used to analyze the models, but also includes brief introductions to many of the applications in different fields of economics. The goal is to give readers the tools to understand the basic models and create their own.For the second edition, major changes have been made to chapter 3, on examples and extensions for the adverse selection model, which now includes more thorough discussions of multiprincipals, collusion, and multidimensional adverse selection, and to chapter 5, on moral hazard, with the limited liability model, career concerns, and common agency added to its topics. Two chapters have been completely rewritten: chapter 7, on the theory of incomplete contracts, and chapter 8, on the empirical literature in the theory of contracts. An appendix presents concepts of noncooperative game theory to supplement chapters 4 and 6. Exercises follow chapters 2 through 5.

Game Theory and the Hebrew Bible

In this unusual book, first published by The MIT Press in 1980 and now updated with a new chapter, Steven Brams applies the mathematical theory of games to the Hebrew Bible. Brams's thesis is that God and the human biblical characters acted rationally—that is, given their preferences and their knowledge of other players' preferences, they made strategy choices that led to the best attainable outcomes.

Beginning with the Creation and focusing on those stories richest in conflict and intrigue, Brams uses elementary game-theoretic tools to elucidate the rational calculations of biblical players and to show precisely the manner in which they sought to achieve their goals. He relies almost exclusively on noncooperative theory, making use of both game tree and matrix forms of games. Brams uses his strategic analyses to build a detailed assessment of God's character and motivations, including the reasons for His frequently wrathful behavior. Brams's insights have application to biblical studies, the philosophy of religion, political theory, and game theory and methodology.

In the new chapter, Brams surveys the literature of the past twenty years on political-strategic interpretations of the Hebrew Bible. He also extends the game-theoretic analysis, using the theory of moves, to study a counterfactual situation—what if Abraham had refused God's command to sacrifice Isaac?—and to examine the rationality of believing in a superior being.

Old Ideas and New Tools

The "oligopoly problem"—the question of how prices are formed when the market contains only a few competitors—is one of the more persistent problems in the history of economic thought. In this book Xavier Vives applies a modern game-theoretic approach to develop a theory of oligopoly pricing.

Vives begins by relating classic contributions to the field—including those of Cournot, Bertrand, Edgeworth, Chamberlin, and Robinson—to modern game theory. In his discussion of basic game-theoretic tools and equilibrium, he pays particular attention to recent developments in the theory of supermodular games. The middle section of the book, an in-depth treatment of classic static models, provides specialized existence results, characterizations of equilibria, extensions to large markets, and an analysis of comparative statics with a view toward applied work. The final chapters examine commitment issues, entry, information transmission, and collusion using a variety of tools: two-stage games, the modeling of competition under asymmetric information and mechanism design theory, and the theory of repeated and dynamic games, including Markov perfect equilibrium and differential games.

Just as macroeconomic models describe the overall economy within a changing, or dynamic, framework, the models themselves change over time. In this text Stephen J. Turnovsky reviews in depth several early models as well as a representation of more recent models. They include traditional (backward-looking) models, linear rational expectations (future-looking) models, intertemporal optimization models, endogenous growth models, and continuous time stochastic models. The author uses examples from both closed and open economies. Whereas others commonly introduce models in a closed context, tacking on a brief discussion of the model in an open economy, Turnovsky integrates the two perspectives throughout to reflect the increasingly international outlook of the field.

This new edition has been extensively revised. It contains a new chapter on optimal monetary and fiscal policy, and the coverage of growth theory has been expanded substantially. The range of growth models considered has been extended, with particular attention devoted to transitional dynamics and nonscale growth. The book includes cutting-edge research and unpublished data, including much of the author's own work.

Theory and Practice

Game theory has become increasingly popular among undergraduate as well as business school students. This text is the first to provide both a complete theoretical treatment of the subject and a variety of real-world applications, primarily in economics, but also in business, political science, and the law. Strategies and Games grew out of Prajit Dutta's experience teaching a course in game theory over the last six years at Columbia University.The book is divided into three parts: Strategic Form Games and Their Applications, Extensive Form Games and Their Applications, and Asymmetric Information Games and Their Applications. The theoretical topics include dominance solutions, Nash equilibrium, backward induction, subgame perfect equilibrium, repeated games, dynamic games, Bayes-Nash equilibrium, mechanism design, auction theory, and signaling. An appendix presents a thorough discussion of single-agent decision theory, as well as the optimization and probability theory required for the course.Every chapter that introduces a new theoretical concept opens with examples and ends with a case study. Case studies include Global Warming and the Internet, Poison Pills, Treasury Bill Auctions, and Final Jeopardy. Each part of the book also contains several chapter-length applications including Bankruptcy Law, the NASDAQ market, OPEC, and the Commons problem. This is also the first text to provide a detailed analysis of dynamic strategic interaction.

Downloadable instructor resources available for this title: solution manual

The greatest strength of this thoroughly revised and expanded edition of Lectures on International Trade is its rigorous algebraic and geometric treatment of the various models and results of trade theory. The authors, who now include Arvind Panagariya, offer both policy insights and empirical applications. They have added nine entirely new chapters as well as new sections to several existing chapters (e.g., a greatly expanded treatment of the growing theory of preferential trade agreements).

Evolutionary game theory is one of the most active and rapidly growing areas of research in economics. Unlike traditional game theory models, which assume that all players are fully rational and have complete knowledge of details of the game, evolutionary models assume that people choose their strategies through a trial-and-error learning process in which they gradually discover that some strategies work better than others. In games that are repeated many times, low-payoff strategies tend to be weeded out, and an equilibrium may emerge.

Larry Samuelson has been one of the main contributors to the evolutionary game theory literature. In Evolutionary Games and Equilibrium Selection, he examines the interplay between evolutionary game theory and the equilibrium selection problem in noncooperative games. After an overview of the basic issues of game theory and a presentation of the basic models, the book goes on to discuss evolutionary stability, the dynamics of sample paths, the ultimatum game, drift, noise, backward and forward induction, and strict Nash equilibria.

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