scholarly journals Knowledge and Equilibrium in Games

1992 ◽  
Vol 6 (4) ◽  
pp. 83-101 ◽  
Author(s):  
Adam Brandenburger
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Decision Theory ◽  
Real World ◽  
Decision Problem ◽  
Noncooperative Game ◽  
Noncooperative Game Theory ◽  
New Directions

This paper describes an approach to noncooperative game theory that aims to capture considerations that exercise the minds of real-world strategists. The most commonly used tool of noncooperative game theory is the Nash equilibrium. This raises the question: Are there assumptions on what the players in a game think—including what they think other players think, and so on—that lead to consideration of Nash equilibrium? The paper provides answers to this, and related, questions. The approach of this paper involves analyzing the decision problem facing each player in a strategic (“interactive”) situation. In addition to grounding game theory in considerations that are of the essence in actual strategic situations, the approach has a number of other objectives: 1) to make game theory more immediately accessible to people who are trained in decision theory but who are not “game theorists” and 2) to make game theory easier to teach to students. Finally, the approach suggests new directions for research into the nature of strategic situations.

scholarly journals Nash Equilibrium and the History of Economic Theory

1999 ◽  
Vol 37 (3) ◽  
pp. 1067-1082 ◽  
Author(s):  
Roger B Myerson
Keyword(s):  
Game Theory ◽  
Economic Theory ◽  
Nash Equilibrium ◽  
Social Science ◽  
Historical Context ◽  
Noncooperative Game ◽  
Noncooperative Game Theory ◽  
History Of Social Science ◽  
History Of

John Nash's formulation of noncooperative game theory was one of the great breakthroughs in the history of social science. Nash's work in this area is reviewed in its historical context to better understand how the fundamental ideas of noncooperative game theory were developed and how they changed the course of economic theory.

scholarly journals New Directions for Modelling Strategic Behavior: Game-Theoretic Models of Communication, Coordination, and Cooperation in Economic Relationships

2016 ◽  
Vol 30 (4) ◽  
pp. 131-150 ◽  
Author(s):  
Vincent P. Crawford
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Strategic Behavior ◽  
Economic Problem ◽  
Noncooperative Game ◽  
Economic Relationships ◽  
Future Developments ◽  
New Directions ◽  
Game Theoretic

In this paper, I discuss the state of progress in applications of game theory in economics and try to identify possible future developments that are likely to yield further progress. To keep the topic manageable, I focus on a canonical economic problem that is inherently game-theoretic, that of fostering efficient coordination and cooperation in relationships, with particular attention to the role of communication. I begin with an overview of noncooperative game theory's principal model of behavior, Nash equilibrium. I next discuss the alternative “thinking” and “learning” rationales for how real-world actors might reach equilibrium decisions. I then review how Nash equilibrium has been used to model coordination, communication, and cooperation in relationships, and discuss possible developments

scholarly journals Nash Equilibrium and the History of Economic Theory

2010 ◽  
pp. 26-43 ◽  
Author(s):  
R. Myerson
Keyword(s):  
Game Theory ◽  
Economic Theory ◽  
Nash Equilibrium ◽  
Historical Context ◽  
Noncooperative Game ◽  
Competitive Behavior ◽  
Noncooperative Game Theory ◽  
History Of Social Science ◽  
Material Goods ◽  
History Of

John Nashs formulation of noncooperative game theory was one of the great breakthroughs in the history of social science. Nashs work in this area is reviewed in its historical context to better understand how the fundamental ideas of noncooperative game theory have been developed and how they have changed the course of economic theory. It is shown in particular how the scope of economics has changed from production and allocation of material goods to the study of rational competitive behavior in any institution of society.

scholarly journals A Cooperative Dual to the Nash Equilibrium for Two-Person Prescriptive Games

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
H. W. Corley ◽  
Phantipa Kwain
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Normal Form ◽  
Fundamental Solution ◽  
Solution Concept ◽  
Alternative Solution ◽  
Noncooperative Game ◽  
Noncooperative Game Theory ◽  
Best Interest

An alternative to the Nash equilibrium (NE) is presented for two-person, one-shot prescriptive games in normal form, where the outcome is determined by an arbiter. The NE is the fundamental solution concept in noncooperative game theory. It is based on the assumption that players are completely selfish. However, NEs are often not played in practice, so we present a cooperative dual as an alternative solution concept by which an arbiter can assign the players' actions. In this dual equilibrium (DE), each player acts in the other's best interest. We formally define prescriptive games and the DE, then summarize the duality relationships between the NE and DE for two players. We also apply the DE to some prescriptive games and compare it to other outcomes.

Dilemmas of Interaction

2018 ◽  
Author(s):  
Peter Vanderschraaf
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Incomplete Information ◽  
Mathematical Theory ◽  
Free Rider ◽  
Noncooperative Game ◽  
Noncooperative Game Theory ◽  
Free Rider Problem ◽  
Game Theoretic ◽  
Principles Of Justice

Problems of interaction, which give rise to justice, are structurally problems of game theory, the mathematical theory of interactive decisions. Five problems of interaction are introduced that are all intrinsically important and that help motivate important parts of the discussions in subsequent chapters: the Farmer’s Dilemma, impure coordination, the Stag Hunt, the free-rider problem, and the choice for a powerless party to acquiesce or resist. Elements of noncooperative game theory essential to analyzing problems of justice are reviewed, including especially games in the strategic and extensive forms, the Nash equilibrium, the Prisoner’s Dilemma, and games of incomplete information. Each of the five motivating problems is reformulated game-theoretically. These game-theoretic reformulations reveal precisely why the agents involved would have difficulty arriving at mutually satisfactory resolutions, and why “solutions” for these problems call for principles of justice to guide the agents’ conduct.

Noncooperative Games

2017 ◽  
Author(s):  
João P. Hespanha
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Robust Design ◽  
Design Problem ◽  
Noncooperative Games ◽  
Network Routing ◽  
Best Interests ◽  
Noncooperative Game ◽  
Noncooperative Game Theory ◽  
Mathematical Solution

This chapter discusses the key principles of noncooperative game theory with the aid of several examples. To characterize a game, several items must be specified; for example, the players are the agents that make decisions. For a mathematical solution to a game, it is also important to make assumptions on the player's rationality, regarding questions such as: Will the players always pursue their best interests to fulfill their objectives? Will the players form coalitions? Will the players trust each other? The chapter proceeds by using the rope-pulling game to examine the motivation and implications of assuming a noncooperative vs. cooperative framework. It also considers the robust design problem and its formalization into a resistive circuit design game, a network routing game, and the Nash equilibrium before concluding with a practice exercise related to the network routing game, complete with solution.

Noncooperative Game Theory

2017 ◽  
Author(s):  
João P. Hespanha
Keyword(s):  
Game Theory ◽  
Computer Science ◽  
Dynamic Games ◽  
Design Methodology ◽  
Noncooperative Game ◽  
Noncooperative Game Theory ◽  
Original Design ◽  
Theoretical Perspectives ◽  
Engineering Designs ◽  
Zero Sum

This book is aimed at students interested in using game theory as a design methodology for solving problems in engineering and computer science. The book 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, the book 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, the book 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. The book looks at such standard topics as zero-sum, non-zero-sum, and dynamic games and includes a MATLAB guide to coding. This book offers students a fresh way of approaching engineering and computer science applications.

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