Evolution, games, and economic behaviour

evolution And Learning In Games Is A Topic Of Current Intense Interest. Evolution Theory Is Widely Viewed As One Of The Most Promising Approaches To Understanding Learning, Bounded Rationality, And Change In Complex Social Environments. This Book Covers The Recent Developments With An Emphasis On Economic Contexts And Applications. Systematically Presenting Both Deterministic And Stochastic Evolutionary Dynamics Which Play An Important Role In Evolutionary Processes, It Also Includes The Recent Stochastic Evolutionary Framework That Has Been Developed (and Applied Widely) In The Last Few Years. Contents......Page 10 1.1 What is an Evolutionary Model......Page 14 1.2 Why Evolutionary Models?......Page 15 1.3 The Plan of What Follows......Page 16 2.1.1 Basic model......Page 24 2.2.1 General definition......Page 26 2.2.2 Alternative interpretations of ESS: monomorphic vs. polymorphic populations......Page 27 2.3.1 Pairwise contests: the Hawk–Dove game......Page 28 2.3.2 Playing the field: the Sex-Ratio game......Page 30 2.4 ESS and Refinements of Nash Equilibrium......Page 33 2.5 The Existence of an ESS......Page 34 2.6.2 Ex ante symmetry with ex post asymmetries......Page 38 2.6.3 Example: the Hawk–Dove game revisited (I)......Page 42 2.6.4 Extensive-form contests......Page 43 2.7.1 The “spite” of an ESS......Page 44 2.7.2 An example of oligopolistic competition......Page 46 2.8 Evolution and Cheap Talk......Page 48 3.1 Introduction......Page 56 3.2.1 The discrete-time case......Page 57 3.2.2 The continuous-time case......Page 58 3.2.3 Properties of the Replicator Dynamics......Page 59 3.3.1 The implicit dynamics of a monomorphic ESS......Page 61 3.3.2 ESS conditions and polymorphic stability......Page 62 3.4 Evolutionary Dynamics and Nash Refinements......Page 65 3.5.1 The Hawk–Dove game revisited (II)......Page 68 3.5.2 The Rock-Scissors-Paper game......Page 69 3.6.1 The model......Page 70 3.6.2 ESS conditions and dynamic evolutionary stability......Page 72 3.7.1 Definitions......Page 74 3.7.2 Necessary conditions for persistence and permanence......Page 75 3.7.3 Sufficient conditions for permanence......Page 77 3.7.4 Average behaviour in permanent systems......Page 79 3.8 Population Genetics......Page 81 3.9 The Prisoner's Dilemma......Page 85 3.9.1 Basic (unperturbed) model......Page 86 3.9.2 Noisy dynamics......Page 89 3.10.1 Preliminaries......Page 92 3.10.2 The model......Page 94 4.1 Introduction......Page 98 4.2 Theoretical Framework......Page 99 4.3.2 Monotonicity properties......Page 100 4.3.3 Some examples......Page 102 4.4.1 Dynamic stability and Nash equilibrium......Page 105 4.4.2 Set stability......Page 108 4.4.3 Long-run regularities......Page 111 4.5.1 Evolution and pay-off dominance......Page 113 4.5.2 Evolution, iterative dominance, and rationalizability......Page 117 4.6 General Evolutionary Processes......Page 119 4.6.2 Dynamic stability and rationality......Page 120 4.7.1 Trading complementarities......Page 122 4.7.2 Risky trading......Page 123 4.8 A Simplified Ultimatum Game......Page 127 4.9 A Hierarchic Model of Cultural Evolution......Page 134 5.1 Introduction......Page 140 5.2 A Simple Example......Page 141 5.3 Theoretical Framework......Page 146 5.4 Analysis......Page 148 5.4.1 Large matching noise......Page 149 5.4.2 Small matching noise......Page 153 5.4.3 On the role of noise in evolutionary models......Page 155 5.4.4 Extensions......Page 157 5.5 Continuous-Time Dynamics......Page 159 5.6.1 Global interaction......Page 163 5.6.2 Local interaction......Page 167 5.7 The Evolution of Walrasian Behaviour......Page 170 6.1 Introduction......Page 174 6.2 General Theoretical Framework......Page 175 6.3 Static Expectations......Page 178 6.4.1 Co-ordination games......Page 179 6.4.2 A simple model of bargaining......Page 183 6.5.1 Introduction......Page 186 6.5.2 Forward induction and efficient co-ordination......Page 187 6.6.1 Introduction......Page 192 6.6.2 Admissible updating rules......Page 193 6.6.3 Equilibrium volatility......Page 194 6.7.1 Introduction......Page 199 6.7.2 The model......Page 200 6.7.3 Narrow sophistication range......Page 203 6.7.4 Wide sophistication range......Page 205 6.7.5 Discussion......Page 206 Afterword......Page 208 7.2 Liouville's Theorem......Page 210 7.3 A Characterization of Negative-Definiteness......Page 211 7.4 Invariant Distribution: Graph Characterization......Page 212 Bibliography......Page 214 E......Page 220 R......Page 221 W......Page 222 This textbook for advanced undergraduate and postgraduate students of Evolutionary Game Theory covers recent developments in the field, with an emphasis on economic contexts and applications. It begins with the basic ideas as they originated within the field of theoretical biology and then proceeds to the formulation of a theoretical framework that is suitable for the study of social and economic phenomena from an evolutionary perspective. Core topics include the Evolutionary Stable Strategy (EES) and Replicator Dynamics (RD), deterministic dynamic models, and stochastic perturbations. A set of short appendices presents some of the technical material referred to in the main text. Evolutionary theory is widely viewed as one of the most promising appraoches to understanding bounded rationality, learning, and change in complex social environments. New avenues of research are suggested by Vega-Redondo, and plentiful exmples illustrate the theory's potential applications. The recent boom experienced by this dscipline makes the book's systematic presentation of its essential contributions vital reading for newcomer to the field."--Publisher description. Evolution theory is widely viewed as one of the most promising approaches to understanding learning in complex social settings. This textbook written with economics students and industrial organisations in mind explains current thinking on the subject