Synopses & Reviews
The book blends together game theory and decision theory and presents the central topics of game theory in a clear and rigorous manner. Numerous applications from economics and other disciplines is used to illustrate the theory. The first chapter is an introduction to single person decision problems which is followed by the chapter on strategic form games (normal form games) with both complete and incomplete information. Among the applications of strategic form games are the Cournot model, the Bertrand model, the Hotelling model and the resource extraction game. This is followed by a chapter on single-person sequential decision problems. The book then moves on to the topic of sequential games (extensive form games) and the concept of sub-game perfect equilibrium. The chapters that follow these are on auctions and bargaining, including both axiomatic and non-cooperative theories of bargaining. There is then a full chapter on repeated games. The penultimate chapter is on sequential games with imperfect information and on equilibrium concepts like sequential equilibrium and Bayesian perfect equilibrium. The final chapter is a summary of the existence results of the various equilibrium concepts and provides detailed proofs of these results. All the chapters include several applications of the concepts discussed in the chapter.
Synopsis
Games and Decision Making, Second Edition, is a unique blend of decision theory and game theory. From classical optimization to modern game theory, authors Charalambos D. Aliprantis and Subir K. Chakrabarti show the importance of mathematical knowledge in understanding and analyzing issues in decision making. Through an imaginative selection of topics, Aliprantis and Chakrabarti treat decision and game theory as part of one body of knowledge. They move from problems involving the individual decision-maker to progressively more complex problems such as sequential rationality, auctions, and bargaining. By building each chapter on material presented earlier, the authors offer a self-contained and comprehensive treatment of these topics.
Successfully class-tested in an advanced undergraduate course at the Krannert School of Management and in a graduate course in economics at Indiana University, Games and Decision Making, Second Edition, is an essential text for advanced undergraduates and graduate students of decision theory and game theory. The book is accessible to students who have a good basic understanding of elementary calculus and probability theory.
About the Author
The late
Charalambos D. Aliprantis was distinguished Professor at the Krannert School of Management at Purdue University. During a career that spanned almost forty years, he published more than one hundred articles in the major journals in economic theory and mathematics and authored half a dozen books on economic theory and mathematics.
Subir K. Chakrabarti is Professor in the Department of Economics at Indiana University and Purdue University at Indianapolis. He has written more than twenty publications, with articles in journals such as Econometrica, Journal of Economic Theory, Journal of Mathematical Economics, International Economic Review, and Journal of Public Economics.
Table of Contents
Preface
Chapter 1. Choices
1.1. Functions
1.2. The optimization problem
1.3. First- and second-order conditions
1.4. Optimizing using the Lagrange method
1.5. Uncertainty and chance
1.6. Decision making under uncertainty
Chapter 2. Decisions and Games
2.1. Two-person matrix games
2.2. Strategic games
2.3. Dominant and dominated strategies
2.4. Solving matrix games with mixed strategies
2.5. Examples of two-person games
2.6. Best responses and Nash equilibria
2.7. Games with incomplete information
2.8. Applications
Chapter 3. Sequential Decisions
3.1. Graphs and trees
3.2. Single-person sequential decisions
3.3. Uncertainty and single-person decisions
Chapter 4. Sequential Games
4.1. The structure of sequential games
4.2. Equilibria in sequential games
4.3. Applications of sequential games
4.4. Solving sequential games with behavior strategies
Chapter 5. Auctions
5.1. Auctions with complete information
5.2. English auctions
5.3. Individual private-value auctions
5.4. Common-value auctions
5.5. Revenue equivalence
Chapter 6. Bargaining
6.1. The Nash solution
6.2. Monotonicity in bargaining
6.3. The core of a bargaining game
6.4. An allocation rule: the Shapley value
6.5. Two-person sequential bargaining
Chapter 7. Repeated Games
7.1. The structure and equilibria of repeated games
7.2. Subgame perfection in finite-horizon repeated games
7.3. Infinite-horizon repeated games
7.4. The Folk theorem and subgame perfect equilibrium
7.5. Applications of repeated and sequential games
Chapter 8. Sequential Rationality
8.1. The market for lemons
8.2. Beliefs and strategies
8.3. Consistency of beliefs
8.4. Expected payoff
8.5. Sequential equilibrium
8.6. Perfect Bayesian equilibrium
8.7. Signaling games
8.8. Applications
Chapter 9. Existence of Equilibria
9.1. Some Mathematical Preliminaries
9.2. Zero-sum games
9.3. Existence of equilibrium in strategic form games
9.4. Existence of equilibrium in sequential games
9.5. Existence of sequential equilibrium
Bibliography