Game Theory for Applied Economists

Citation

Gibbons, R. (1992). Game Theory for Applied Economists. Princeton University Press.

Chapter Summary

The book is a short text of 288 pages, organised into four chapters that follow a simple grid. According to the publisher, it covers four classes of games and four matching notions of equilibrium: static games of complete information and Nash equilibrium, dynamic games of complete information and subgame-perfect Nash equilibrium, static games of incomplete information and Bayesian Nash equilibrium, and dynamic games of incomplete information and perfect Bayesian equilibrium. The aim, as the publisher puts it, is to address scholars in applied fields of economics who want a serious and thorough discussion of game theory but may find other works too abstract. Applications are emphasised at least as much as pure theory, and formal arguments about abstract games play a minor role. The applications illustrate model building, the translation of an informal description of a multi-person decision situation into a formal game. Each chapter ends with further reading, problems and references.

Chapter 1: Static Games of Complete Information

The first chapter considers games in which players choose actions simultaneously and then receive payoffs, with each player's payoff function common knowledge. Section 1.1 (Basic Theory: Normal-Form Games and Nash Equilibrium) introduces the normal-form representation, iterated elimination of strictly dominated strategies, and the motivation and definition of Nash equilibrium. Section 1.2 (Applications) works through four models: Cournot duopoly, Bertrand duopoly, final-offer arbitration and the problem of the commons. Section 1.3 (Advanced Theory: Mixed Strategies and Existence of Equilibrium) defines mixed strategies and discusses the existence of Nash equilibrium. The chapter itself says that Section 1.3 is not a prerequisite for the applications in Section 1.2, though mixed strategies and existence do occasionally reappear later.

Chapter 2: Dynamic Games of Complete Information

Chapter 2 moves to sequential play and has five main sections. Section 2.1 treats games of complete and perfect information: backwards induction, the Stackelberg model of duopoly, wages and employment in a unionised firm, and sequential bargaining. Section 2.2 treats two-stage games of complete but imperfect information, introducing subgame perfection through bank runs, tariffs and imperfect international competition, and tournaments. Section 2.3 is on repeated games, beginning with the two-stage repeated game and the infinitely repeated game, then applying them to collusion between Cournot duopolists, efficiency wages and time-consistent monetary policy. Section 2.4 gives the extensive-form representation of games and the general definition of subgame-perfect Nash equilibrium.

Chapter 3: Static Games of Incomplete Information

The third chapter introduces static Bayesian games and Bayesian Nash equilibrium (Section 3.1), starting from an example of Cournot competition under asymmetric information and moving to the normal-form representation and the definition of the equilibrium. Section 3.2 gives applications: mixed strategies revisited, an auction and a double auction. Section 3.3 presents the revelation principle.

Chapter 4: Dynamic Games of Incomplete Information

The last chapter, running from page 173 to 253, introduces perfect Bayesian equilibrium (Section 4.1) and spends much of its length on signalling games (Section 4.2): equilibrium in signalling games, job-market signalling, corporate investment and capital structure, and monetary policy. Section 4.3 collects other applications of perfect Bayesian equilibrium: cheap-talk games, sequential bargaining under asymmetric information, and reputation in the finitely repeated prisoners' dilemma. Section 4.4 turns to refinements of perfect Bayesian equilibrium.

Key Concepts

Chapter 1: Static Games of Complete Information

• Normal-form representation: a game specified by its players, their strategies and the payoff from each combination of strategies.
• Strictly dominated strategy: a strategy that rational players would not play, used to simplify some games.
• Nash equilibrium: a solution concept that gives much tighter predictions than dominance in a broad class of games.
• Mixed strategy: a randomised strategy, interpreted as one player's uncertainty about what another will do.

Chapter 2: Dynamic Games of Complete Information

• Backwards induction: solving a sequential game from its last move.
• Subgame perfection: the equilibrium notion for dynamic games of complete information.
• Repeated games: stage games played over time, in two-stage and infinitely repeated forms.
• Extensive-form representation: the game-tree description of sequential play.

Chapter 3: Static Games of Incomplete Information

• Static Bayesian game: a simultaneous-move game in which a player is uncertain about another's payoff function.
• Bayesian Nash equilibrium: the solution concept for such games.
• Revelation principle: a result presented in Section 3.3, following the auction applications.

Chapter 4: Dynamic Games of Incomplete Information

• Perfect Bayesian equilibrium: the solution concept for sequential games with incomplete information.
• Signalling game: a game in which an informed player moves first and an uninformed player responds.
• Cheap talk: communication that is costless to the sender.
• Refinements: further restrictions on perfect Bayesian equilibrium.

Critical Analysis

Strengths

• A clear organising grid. The four chapters pair a class of games with an equilibrium concept, so each new idea has a definite place. This is the structure the publisher uses to describe the book.
• Applications drive the theory. Each theoretical section is followed by economic models: Cournot, Bertrand, Stackelberg, bank runs, tariffs, tournaments, efficiency wages, auctions, job-market signalling and others. Readers see how to translate an informal problem into a game.
• Compact length. At 288 pages it can be covered in a single course, and Chapter 1 itself says that its advanced theory section is not needed to follow the applications.
• Support for practice. Every chapter closes with further reading, problems and references.

Limitations

• Emphasis on economic applications. The publisher says that abstract formal arguments play a minor role, so readers who want proofs and the foundations of solution concepts will need a more theoretical text.
• Date. The book was published in 1992, and developments in game theory after that date are not included.
• Economic scope. The applications are those of applied economics (industrial organisation, labour, macroeconomics, auctions); the book is not a source on political or social applications.

Where It Fits in the Course

Among the game theory books on the list, Gibbons is the applications-oriented graduate text. Binmore's Game Theory: A Very Short Introduction and Dixit and Nalebuff's The Art of Strategy are non-technical introductions for general readers, while Dixit, Skeath and McAdams's Games of Strategy teaches the main solution concepts with minimal mathematics through examples from economics, politics, business and everyday life. Any of these makes a good first pass before Gibbons.

Osborne and Rubinstein's A Course in Game Theory is a concise graduate book that gives precise definitions and proofs and emphasises the interpretation of solution concepts. The two complement each other: Gibbons for how to build and solve models in economic applications, Osborne and Rubinstein for the foundations.

How to Use This Book

The publisher addresses scholars in applied fields of economics who will construct or consume game-theoretic models, and the book suits graduate students and advanced undergraduates in economics. Familiarity with the basic microeconomic models behind the applications, such as Cournot and Bertrand duopoly, makes the examples easier to follow.

A practical plan:

• Core: Sections 1.1 and 1.2, then Chapter 2 through Section 2.2 and the basics of repeated games in Section 2.3. These give Nash equilibrium and subgame perfection with the standard models.
• Next: Section 3.1, the auction in Section 3.2, then Section 4.1 and the signalling games of Section 4.2.
• Optional on a first pass: Section 1.3 (advanced theory), Sections 2.4 and 3.3, and the refinements in Section 4.4.
• Practice: work the problems at the end of each chapter, and follow the further reading to the original papers behind the applications.