EVOLUTIONARY DYNAMICS AND EXTENSIVE FORM GAMES
CONTENTS 1 INTRODUCTION EXTENSIVE FORM VERSUS NORMAL FORM BIOLOGY VERSUS ECONOMICS IMITATION ORGANIZATIONAL MATTERS NOTES 2 SYMMETRIC NORMAL FORM GAMES THE REPLICATOR DYNAMIC DYNAMICS FOR TWO-STRATEGY GAMES MONOTONE SELECTION DYNAMICS FICTITIOUS PLAY AND BEST RESPONSE DYNAMIC CONVERGENCE AND STABILITY: NE AND ESS THREE-STRATEGY GAME DYNAMICS 2 6 1 ROCK–SCISSORS–PAPER GAMES 2 6 2 ESSETS AND NE COMPONENTS 2 6 3 MORE THREE-STRATEGY GAMES DYNAMIC STABILITY FOR GENERAL GAMES NATURAL SELECTION AT A SINGLE LOCUS 2 8 1 DISCRETE-TIME VIABILITY SELECTION 2 8 2 CONTINUOUS-TIME NATURAL SELECTION ONE-STAGE SIMULTANEITY GAMES 2 10 MULTI-ARMED BANDITS 2 11 APPENDIX 2 12 NOTES 3 BIMATRIX GAMES NASH EQUILIBRIA AND STRICT EQUILIBRIUM SETS BIMATRIX REPLICATOR AND BEST RESPONSE DYNAMICS 3 2 1 THE OWNER-INTRUDER GAME DYNAMICS FOR TWO-STRATEGY BIMATRIX GAMES 3 3 1 NONDEGENERATE BIMATRIX GAMES 3 3 2 DEGENERATE BIMATRIX GAMES SYMMETRIZED BIMATRIX GAMES 3 4 1 THE SYMMETRIZED BIMATRIX REPLICATOR DYNAMIC 3 4 2 THE SYMMETRIZED BEST RESPONSE DYNAMIC BIMATRIX MONOTONE SELECTION DYNAMICS 4 ASYMMETRIC GAMES THE NORMAL FORM THE EXTENSIVE FORM: NE AND ESSETS 4 2 1 AN AGE-STRUCTURED OWNER-INTRUDER GAME SESETS AND AGENT NORMAL FORMS DYNAMICS AND THE WRIGHT MANIFOLD 4 4 1 THE REPLICATOR DYNAMIC AND SUBGAMES 4 4 2 BEST RESPONSE DYNAMICS TRULY ASYMMETRIC TWO-PLAYER GAMES 4 5 1 THE AGE-STRUCTURED OWNER-INTRUDER GAME DYNAMIC TRULY SYMMETRIC TWO-PLAYER GAMES 4 6 1 A TRULY SYMMETRIC GAME DYNAMIC COUNTEREXAMPLE 4 6 2 PARALLEL BANDITS ASYMMETRIC GAMES WITH TWO ROLES 4 7 1 A FAMILY OF ASYMMETRIC GAMES 4 7 2 TWO-SPECIES EVOLUTIONARILY STABLE STRATEGIES A HIERARCHICAL HAWK-DOVE GAME APPENDIX A 4 10 APPENDIX B 4 11 NOTES 5 NATURAL SELECTION WITH MULTIPLE LOCI CONTINUOUS-TIME SELECTION-RECOMBINATION SYMMETRIC EXTENSIVE FORM WITH ADDITIVE FITNESS RECOMBINATION SELECTION AND RECOMBINATION 6 EXTENSIVE FORM GAMES N-PLAYER EXTENSIVE FORM GAMES 6 1 1 STRATEGIES AND PAYOFFS 6 1 2 NASH EQUILIBRIA, SUBGAMES, AND BACKWARD INDUCTION NORMAL FORMS AND THE REPLICATOR DYNAMIC THE WRIGHT MANIFOLD AND REPLICATOR DYNAMIC SYMMETRIC EXTENSIVE FORM GAMES APPENDIX 7 SIMULTANEITY GAMES ELEMENTARY TWO-STAGE SIMULTANEITY GAMES TWO-STAGE TWO-STRATEGY GAMES 7 2 1 TWO-STAGE TWO-STRATEGY REPEATED GAMES 7 2 2 SYMMETRIC SIGNALING GAMES 7 2 3 CHEAP TALK GAMES ASYMPTOTIC STABILITY OF PERVASIVE NE 7 3 1 SIMULTANEITY GAMES WITH NO ASYMMETRIC SUBGAMES 7 3 2 SIMULTANEITY GAMES WITH ASYMMETRIC SUBGAMES 7 3 3 SIMULTANEITY GAMES WITH MOVES BY NATURE THE WAR OF ATTRITION 7 4 1 THE DISCRETE WAR OF ATTRITION 7 4 2 THE CONTINUOUS WAR OF ATTRITION 7 4 3 THE DISCRETE WAR OF AGGRESSION THE FINITELY REPEATED PRISONER’S DILEMMA GAME 7 5 1 THE REPLICATOR AND MONOTONE SELECTION DYNAMICS 7 5 2 THE BEST RESPONSE DYNAMIC AND FICTITIOUS PLAY APPENDIX B: MAXIMAL ATTRACTOR 8 PERFECT INFORMATION GAMES ELEMENTARY PERFECT INFORMATION GAMES EQUILIBRIUM SELECTION: DYNAMIC APPROACH 8 2 1 THE REPLICATOR AND MONOTONE SELECTION DYNAMICS 8 2 2 FICTITIOUS PLAY AND BEST RESPONSE DYNAMIC 8 2 3 BEHAVIOR STRATEGY FICTITIOUS PLAY THE CENTIPEDE GAME 8 3 1 CENTIPEDE GAMES OF LENGTHS TWO AND THREE EXTENSIVE FORM BANDITS 8 4 1 THE CENTIPEDE BANDIT APPENDIX B 9 SUBGAME MONOTONICITY MONOTONE TRAJECTORIES SUBGAME MONOTONE TRAJECTORIES AN IMITATION EXAMPLE DISCUSSION