Game Theory in Biology: Concepts and Frontiers

Description

The principles of game theory apply to a wide range of topics in biology. This book presents the central concepts in evolutionary game theory and provides an authoritative and up-to-date account. The focus is on concepts that are important for biologists in their attempts to explain observations. This strong connection between concepts and applications is a recurrent theme throughout the book which incorporates recent and traditional ideas from animal psychology, neuroscience, and machine learning that provide a mechanistic basis for behaviours shown by players of a game. The approaches taken to modelling games often rest on idealized and unrealistic assumptions whose limitations and consequences are not always appreciated. The authors provide a novel reassessment of the field, highlighting how to overcome limitations and identifying future directions. Game Theory in Biology is an advanced textbook suitable for graduate level students as well as professional researchers (both empiricists and theoreticians) in the fields of behavioural ecology and evolutionary biology. It will also be of relevance to a broader interdisciplinary audience including psychologists and neuroscientists. Cover Game Theory in Biology: Concepts and Frontiers Copyright Contents Acknowledgements 1: Setting the Scene 1.1 Introduction 1.2 Frequency Dependence 1.3 The Modelling Approach 1.4 Scope of the Field and Challenges 1.5 Approach in This Book 1.5.1 Challenges 2: Central Concepts 2.1 Actions, States, and Strategies 2.1.1 Actions 2.1.2 States 2.1.3 Strategies 2.2 The Phenotypic Gambit 2.3 Invasion Fitness 2.4 Evolutionary Endpoints 2.5 Fitness Proxies 2.6 From Strategies to Individuals 3: Standard Examples 3.1 Contributing to the Common Benefit at a Cost 3.2 Helping Others: The Prisoner’s Dilemma Game 3.3 The Tragedy of the Commons 3.4 Biparental Care: The Parental Effort Game 3.4.1 Parents Can Respond to Each Other 3.5 Contest Over a Resource: The Hawk–Dove Game 3.5.1 Lethal Fighting 3.5.2 Information is Important in Real Fights 3.6 The Evolution of Signalling: From Cue to Signal 3.7 Coordination Games 3.8 Produce Sons or Daughters? The Sex-Allocation Game 3.9 Playing the Field 3.10 Dispersal as a Means of Reducing Kin Competition 3.11 Threshold Decisions 3.11.1 Pairwise Contests Where Individuals Know Their Own Fighting Ability 3.11.2 Alternative Male Mating Tactics For Pacific Salmon 3.11.3 Environmental Sex Determination 3.12 Assessment and Bayesian Updating 3.12.1 A Model of Animal Conflict with Assessment 3.12.2 How the Model Can Be Used 3.13 Exercises 4: Stability Concepts: Beyond Nash Equilibria 4.1 Evolutionarily Stable Strategies 4.1.1 Stability in the Hawk–Dove Game 4.1.2 Playing the Field 4.1.3 Illustration of Stability for a Continuous Trait: A Predator Inspection Game 4.1.4 The Strength of Selection 4.2 Adaptive Dynamics 4.2.1 Convergence Stability 4.2.2 The Slope of the Best Response Function and Convergence Stability 4.2.3 Pairwise Invasibility Plots 4.3 Evolution to a Fitness Minimum 4.3.1 Two Local Habitats Linked by Dispersal 4.3.1.1 Two-Habitat Model 4.3.2 Evolutionary Branching 4.4 Replicator Dynamics 4.5 Games Between Relatives 4.5.1 The Evolution of Helping 4.5.2 Hawk–Dove Game Between Relatives 4.5.3 Parent–Offspring Conflict 4.6 Exercises 5: Learning in LargeWorlds 5.1 Reinforcement Learning 5.1.1 The Actor–Critic Approach 5.1.2 Average Actor–Critic Dynamics in a Population 5.2 Learning and the Hawk–Dove Game 5.3 Learning in a Game of Joint Benefit of Investment 5.4 A Dominance Game 5.4.1 Case of No Observations and No Learning 5.4.2 Learning and Primary Rewards 5.4.3 Slow Learning Without Observations 5.4.4 Evolution of Learning with Observations 5.5 Approaches to Learning in Game Theory 5.5.1 Convergence towards an Endpoint of a Game 5.5.2 Large and Small Worlds 5.6 Exercises 6: Co-evolution of Traits 6.1 Stability in More than One Dimension 6.2 Role Asymmetries 6.2.1 Convergence Stability with a Role Asymmetry 6.2.2 Example: Territory Owner Versus Intruder 6.2.3 Real Owner–Intruder Contests 6.3 The Evolution of Anisogamy 6.3.1 Gamete Size Versus Number 6.4 Evolution of Abilities and Role Specialization 6.4.1 Co-evolution of Parental Effort and Ability to Care 6.5 Learning and Individual Specialization 6.6 Co-evolution of Prosociality and Dispersal 6.6.1 Model: Group Defence and Dispersal to Empty Areas 6.7 Co-evolution of Species 6.7.1 Parasite–Host and Predator–Prey Interactions 6.8 Concluding Comments 6.9 Exercises 7: Variation, Consistency, and Reputation 7.1 Variation has Consequences 7.2 Variation and the Stability of Equilibria 7.3 Taking a Chance 7.3.1 Taking Risks in a Finitely Repeated Prisoner’s Dilemma Game 7.4 Signalling and the Handicap Principle 7.4.1 Males Signal Parental Ability, Females Respond with Clutch Size 7.4.1.1 The Handicap Principle 7.4.1.2 Costs of Deviation 7.5 Reputation 7.6 Indirect Reciprocity 7.7 Differences Select for Social Sensitivity 7.8 Markets 7.8.1 A Model of the Nectar Market 7.9 Choosiness, Assortment, and Cooperation 7.10 Commitment 7.10.1 A Model of the Co-evolution of Choosiness and Commitment 7.11 Exercises 8: Interaction, Negotiation, and Learning 8.1 Interaction over Time 8.2 Information and the Order of Choice 8.2.1 Extensive Versus Normal Form 8.3 Credible Threats and Strategic Commitment 8.4 Negotiation between Partners 8.5 Evolution of Cognitive Bias 8.5.1 Common Interest 8.6 Social Dominance 8.6.1 The Dominance Game with Individual Recognition 8.6.2 Rapid Learning for the Actor 8.6.3 Effect of Group Size 8.7 Assessment in Contests 8.7.1 The Sequential Assessment Game 8.7.2 Decision-making as a Neural Random Walk 8.8 Outlook: Games with Interaction over Time 8.8.1 Examples of Fruitful Areas of Application 8.8.2 Behavioural Mechanisms in Large and Small Worlds 8.8.3 Evolutionary Stability for Large-worlds Models 8.9 Exercises 9: Games Embedded in Life 9.1 Self-consistency 9.2 The Shadow of the Future, and the Past 9.3 Resident Strategy Affects Future Opportunities 9.3.1 Care for Young or Desert 9.4 Dependence on Future Actions 9.4.1 Model of Repeated Contests 9.4.2 Reproductive Value and the Emergence of Costs 9.4.3 Assessment and Plastic Adjustment 9.5 Territorial Defence and the Desperado Effect 9.5.1 Owner–Intruder Contests with Assessment and Learning 9.6 State-dependent Ideal Free Distributions 9.6.1 Survival Over the Winter 9.6.2 Further Dynamic Games 9.7 Is it Worth it? 9.8 Exercises 10: Structured Populations and Games over Generations 10.1 Invasion Fitness for Structured Populations 10.2 Offspring Quality versus Number 10.3 Reproductive Value Maximization 10.4 Sex Allocation as a Game over Generations 10.4.1 The Shaw–Mohler Fitness Proxy 10.4.2 Quality-dependent Sex Allocation 10.4.3 Empirical Evidence 10.5 The Fisher Runaway Process 10.6 Maximizing Lifetime Reproductive Success 10.6.1 Reproductive Scheduling 10.7 Dispersal 10.8 Evolutionary Analysis in Structured Populations 10.9 Exercises 11: Future Perspectives 11.1 Phylogeny 11.2 Behavioural Mechanisms in LargeWorlds 11.2.1 Which Parameters are Tuned by Evolution? 11.2.2 Mechanisms and Flexibility 11.3 Ontogeny and the Acquisition of Behaviour Appendix A: Summary of Notation Appendix B: Solutions to Exercises References Index