Rational Choice

This book offers a rigorous, concise, and nontechnical introduction to some of the fundamental insights of rational choice theory. It draws on formal theories of microeconomics, decision making, games, and social choice, and on ideas developed in philosophy, psychology, and sociology. Itzhak Gilboa argues that economic theory has provided a set of powerful models and broad insights that have changed the way we think about everyday life. He focuses on basic insights of the rational choice paradigm—the general conceptualization rather than a particular theory—that survive recent (and well-justified) critiques of economic theory's various failures. Gilboa explains the main concepts in language accessible to the nonspecialist, offering a nonmathematical guide to some of the main ideas developed in economic theory in the second half of the twentieth century. Chapters cover feasibility and desirability, utility maximization, constrained optimization, expected utility, probability and statistics, aggregation of preferences, games and equilibria, free markets, and rationality and emotions. Online appendixes offer a survey of relevant mathematical concepts, a rigorous exposition of the formal models described in the book, exercises and problems, and solutions. These materials are useful supplements to the book for classroom use. Cover Page 1 Title Page 4 ISBN 9780262014007 5 Contents 8 Preface 14 Suggested Reading 18 Microeconomic Theory 18 Decision Theory 18 Game Theory 19 Social Choice Theory 19 I Optimization 20 1 Feasibility and Desirability 22 1.1 Examples 22 1.2 Separating Can from Want 22 1.3 What Is Meant by Rational? 24 1.4 Uncertainty 25 1.5 Zen and the Absurd 26 1.6 On Theories and Paradigms 28 2 Utility Maximization 30 2.1 Example 30 2.2 Two Points 36 2.3 Interpretations 36 2.3.1 Normative 37 2.3.2 Descriptive 38 2.3.3 Metascientific 39 2.4 Measurement Issues 40 2.5 Utility and Disutility 41 3 Constrained Optimization 44 3.1 General Framework 44 3.2 Example: The Consumer Problem 46 3.3 Marginality Principle 48 II Risk and Uncertainty 52 4 Expected Utility 54 4.1 Examples 54 4.2 Expected Value Maximization 55 4.2.1 i.i.d. Random Variables 55 4.2.2 Law of Large Numbers 56 4.2.3 Practical Meaning of Expected Value 57 4.3 Expected Utility Maximization 58 4.3.1 von Neumann and Morgenstern's Theorem 58 4.3.2 Uniqueness of Utility 59 4.3.3 Risk Aversion 60 4.3.4 Prospect Theory 62 4.4 Elicitation of Utility 63 4.5 From Simple to Complex 65 5 Probability and Statistics 68 5.1 What Is Probability? 68 5.2 Relative Frequencies as Objective Probabilities 71 5.3 Subjective Probabilities 73 5.4 Statistical Pitfalls 75 5.4.1 Confounding Conditional Probabilities 76 5.4.2 Biased Samples 78 5.4.3 Regression to the Mean 80 5.4.4 Correlation and Causation 83 5.4.5 Statistical Significance 86 III Group Choices 90 6 Aggregation of Preferences 92 6.1 Summation of Utilities 92 6.2 Condorcet's Paradox 96 6.3 Impossibility Theorems 97 6.3.1 Arrow's Theorem 97 6.3.2 Scoring Rules and Grading Systems 99 6.3.3 Gibbard-Satterthwaite's Theorem 102 6.3.4 An Argument for Approval Voting 104 6.3.5 Conclusion 104 6.4 Pareto Optimality/Efficiency 104 6.5 Limitations of Pareto Optimality 106 6.5.1 Silent on Equality 107 6.5.2 A Partial Order 107 6.5.3 Subjective Beliefs 109 7 Games and Equilibria 110 7.1 Prisoner's Dilemma 110 7.1.1 The Basic Story 110 Game 1. Prisoner's Dilemma 111 7.1.2 Dominated Strategies 111 Game 2. A Variant of Prisoner's Dilemma 112 7.1.3 Back to Prisoner's Dilemma 114 7.1.4 The Meaning of Utility 114 7.1.5 Main Lessons 116 7.1.6 Changing the Rules of the Game 118 Game 3. Prisoner's Dilemma with Payoffs Modified by Punishment 118 7.1.7 Repetition 119 7.1.8 Kant's Categorical Imperative and the Golden Rule 120 Game 4. Prisoner's Dilemma Played with the Mirror Image 121 7.2 Nash Equilibria 122 7.2.1 Definition 122 7.2.2 Justifications 122 7.2.3 Mixed Strategies 124 Game 5. Matching Pennies 124 7.3 Equilibrium Selection 126 7.3.1 Stylized Examples 126 Game 6. Pure Coordination 1 126 Game 7. Pure Coordination 2 127 Game 8. Battle of the Sexes 127 Game 9. Stag Hunt 128 7.3.2 Real-Life Examples 128 7.4 The Power of Commitment 130 Game 10. Battle of the Sexes after Elimination of One Column 130 7.5 Common Knowledge 132 7.6 Extensive Form Games 132 7.7 Perfectness and Credible Threats 133 7.7.1 Backward Induction 136 8 Free Markets 138 8.1 Example: The Case for Globalization 138 8.2 The First Welfare Theorem 142 8.3 Limitations of Free Markets 148 8.3.1 Externalities and Public Goods 148 8.3.2 Market Power 149 8.3.3 Asymmetric Information 149 8.3.4 Existence versus Convergence 151 8.3.5 Formation of Preference 152 8.3.6 Irrational Behavior 152 8.3.7 What Is Measured by Utility? 153 8.3.8 A Limitation of Pareto Optimality 153 8.4 Example 154 IV Rationality and Emotions 156 9 Evolutionary View of Emotions 158 10 Utility and Well-Being 162 10.1 Money Isn't Happiness 162 10.2 Qualifications 164 10.2.1 The Validity of Questionnaires 164 10.2.2 Don t Push Others off the Hedonic Treadmill 166 10.2.3 People Don't Adjust to Everything 167 Epilogue 168 Notes 170 Chapter 1 170 Chapter 3 170 Chapter 4 170 Chapter 5 170 Chapter 6 171 Chapter 7 171 Chapter 8 172 Chapter 9 172 Chapter 10 172 Index 174 Appendixes 178 A Mathematical Preliminaries 178 A.1 Notation 178 A.2 Sets 179 A.3 Relations and Functions 181 A.4 Cardinalities of Sets 184 A.5 Calculus 187 A.5.1 Limits of Sequences 187 A.5.2 Limits of Functions 188 A.5.3 Continuity 189 A.5.4 Derivatives 190 A.5.5 Partial Derivatives 191 A.6 Topology 192 A.7 Probability 193 A.7.1 Basic Concepts 193 A.7.2 Random Variables 195 A.7.3 Conditional Probabilities 197 A.7.4 Independence and i.i.d. Random Variables 199 A.7.5 Law(s) of Large Numbers 202 LLN and Relative Frequencies 203 B Formal Models 204 B.1 Utility Maximization 204 B.1.1 Definitions 204 B.1.2 Axioms 205 B.1.3 Result 207 B.1.4 Generalization to a Continuous Space 207 B.2 Convexity 209 B.2.1 Convex Sets 209 B.2.2 Convex and Concave Functions 209 B.2.3 Quasi-convex and Quasi-concave Functions 212 B.3 Constrained Optimization 214 B.3.1 Convex Problems 214 B.3.2 Example: The Consumer Problem 215 B.3.3 Algebraic Approach 215 B.3.4 Geometric Approach 216 B.3.5 Economic Approach 218 B.3.6 Comments 219 B.4 vNM’s Theorem 219 B.4.1 Setup 219 B.4.2 The vNM Axioms 220 B.4.3 Continuity 221 B.4.4 Independence 222 B.4.5 The Theorem 223 B.5 Ignoring Base Probabilities 223 B.6 Arrow’s Impossibility Theorem 225 B.7 Nash Equilibrium 227 C Exercises 230 Chapter 1 Feasibility and Desirability 230 Chapter 2 Utility Maximization 231 Chapter 3 Constrained Optimization 232 Chapter 4 Expected Utility 233 Chapter 5 Probability and Statistics 234 Chapter 6 Aggregation of Preferences 235 Chapter 7 Games and Equilibria 236 Game 6. Pure Coordination 1 237 Game 7. Pure Coordination 2 237 Game 8. Battle of the Sexes 237 Chapter 8 Free Markets 238 D Solutions 240 Chapter 1 Feasibility and Desirability 240 Chapter 2 Utility Maximization 243 Chapter 3 Constrained Optimization 251 Chapter 4 Expected Utility 256 Chapter 5 Probability and Statistics 265 Chapter 6 Aggregation of Preferences 270 Chapter 7 Games and Equilibria 273 Game 6. Pure Coordination 1 277 Game 7. Pure Coordination 2 278 Game 8. Battle of the Sexes 278 Chapter 8 Free Markets 283 0262014009,9780262014007 A nontechnical, concise, and rigorous introduction to the rational choice paradigm, focusing on basic insights applicable in fields ranging from economics to philosophy. This book offers a rigorous, concise, and nontechnical introduction to some of the fundamental insights of rational choice theory. It draws on formal theories of microeconomics, decision making, games, and social choice, and on ideas developed in philosophy, psychology, and sociology. Itzhak Gilboa argues that economic theory has provided a set of powerful models and broad insights that have changed the way we think about everyday life. He focuses on basic insights of the rational choice paradigm—the general conceptualization rather than a particular theory—that survive recent (and well-justified) critiques of economic theory's various failures. Gilboa explains the main concepts in language accessible to the nonspecialist, offering a nonmathematical guide to some of the main ideas developed in economic theory in the second half of the twentieth century. Chapters cover feasibility and desirability, utility maximization, constrained optimization, expected utility, probability and statistics, aggregation of preferences, games and equilibria, free markets, and rationality and emotions. Online appendixes offer additional material, including a survey of relevant mathematical concepts. "This book offers a rigorous, concise, and nontechnical introduction to some of the fundamental insights of rational choice theory. It draws on formal theories of microeconomics, decision making, games, and social choice, and on ideas developed in philosophy, psychology, and sociology. Itzhak Gilboa argues that economic theory has provided a set of powerful models and broad insights that have changed the way we think about everyday life. He focuses on basic insights of the rational choice paradigm - the general conceptualization rather than a particular theory - that survive recent(and well-justified) critiques of economic theory's various failures. Gilboa explains the main concepts in language accessible to the nonspecialist, offering a nonmathematical guide to some of the main ideas developed in economic theory in the second half of the twentieth century." "Chapters cover feasibility and desirability, utility maximization, constrained optimization, expected utility, probability and statistics, aggregation of preferences, games and equilibria, free markets, and rationality and emotions. Online appendixes offer a survey of relevant mathematical concepts, a rigorous exposition of the formal models described in the book, exercises and problems, and solutions. These materials are useful supplements to the book for classroom use."--Contraportada This Text Offers A Rigorous, Concise, And Nontechnical Introduction To Some Of The Fundamental Insights Of Rational Choice Theory. It Draws On Formal Theories Of Microeconomics, Decision Making, Games, And Social Choice, And On Ideas Developed In Philosophy, Psychology, And Sociology. Feasibility And Desirability -- Utility Maximization -- Constrained Optimization -- Expected Utility -- Probability And Statistics -- Aggregation Of Preferences -- Games And Equilibria -- Free Markets -- Evolutionary View Of Emotions -- Utility And Well-being Itzhak Gilboa. Includes Bibliographical References And Index.