Solution concepts for noncooperative games

This chapter focuses on the analysis and “solution” of noncooperative games. Any predictions one makes about how a game will be played must depend on the characteristics of the individuals playing the game. The theories that the chapter presents proceed on the presumption that all the players in the game are “rational,” that each credits their rivals with “rationality,” that each believes that all rivals credit their rivals with “rationality,” and so forth. The objective is to predict how people act in gamelike settings. The ground rules in noncooperative game theory are that the description of the game should include all relevant opportunities for the players. One of the hardest things to handle in this regard is the possibility that the players can communicate.

A Course in Microeconomic Theory

This book is a text in microeconomics that is both challenging and “user-friendly.” The work is designed for the first-year graduate microeconomic theory course and is accessible to advanced undergraduates as well. Placing unusual emphasis on modern noncooperative game theory, it provides the student and instructor with a unified treatment of modern microeconomic theory — one that stresses the behavior of the individual actor (consumer or firm) in various institutional settings. The author has taken special pains to explore the fundamental assumptions of the theories and techniques studied, pointing out both strengths and weaknesses. The book begins with an exposition of the standard models of choice and the market, with extra attention paid to choice under uncertainty and dynamic choice. General and partial equilibrium approaches are blended, so that the student sees these approaches as points along a continuum. The work then turns to more modern developments. Readers are introduced to noncooperative game theory and shown how to model games and determine solution concepts. Models with incomplete information, the folk theorem and reputation, and bilateral bargaining are covered in depth, followed by exploration of information economics. A closing discussion concerns firms as organizations and gives readers a taste of transaction-cost economics.

Bilateral bargaining

This chapter examines how, after discussing monopoly, many principles and intermediate microeconomics books move on to the cases of monopsony (one buyer and many sellers) and bilateral monopoly (one buyer and one seller). The analysis of monopsony is straightforward after monopoly. The monopsonist, taking their supply curve as given, equates the marginal value of the factor to them with the “marginal factor cost.” Then there is a paragraph or two about bilateral monopoly. The chapter considers what noncooperative game theory has to offer to this situation. This is a case where institutions matter (according to the theory), and rather more than seems sensible, although the extreme and unintuitive sensitivity to institutional form that one sees in the theory may be attributable to the starkness of the models in terms of what players know about each other. The chapter then looks at the problem of bilateral bargaining.

Dilemmas of Interaction

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 Game Theory

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.