Games and Decision Making

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. New to this Edition * Chapter 2 includes new sections on two-person games, best-response strategies, mixed strategies, and incomplete information * Chapter 4 has been expanded to provide new material on behavior strategies and applications * The chapter on auctions (5) includes a new section on revenue equivalence * Offers two new chapters, on repeated games (7) and existence results (9) * New applications have been added to all the chapters

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

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.