Game Theory Basics

✍ Scribed by Bernhard von Stengel

• Publisher: Cambridge University Press
• Year: 2021
• Tongue: English
• Leaves: 376
• Category: Library

✦ Table of Contents

Cover
Half-title Page
Title Page
Copyright Page
Contents
Preface
Aims and Contents
Mathematical and Scholarly Level
Acknowledgments
1 Nim and Combinatorial Games
1.1 Prerequisites and Learning Outcomes
1.2 Nim
1.3 Top-down Induction
1.4 Game Sums and Equivalence of Games
1.5 Nim, Poker Nim, and the Mex Rule
1.6 Sums of Nim Heaps
1.7 Finding Nim Values
1.8 A Glimpse of Partizan Games
1.9 Further Reading
1.10 Exercises for Chapter 1
2 Congestion Games
2.1 Prerequisites and Learning Outcomes
2.2 Introduction: The Pigou Network
2.3 The Braess Paradox
2.4 Definition of Congestion Games
2.5 Existence of Equilibrium in a Congestion Game
2.6 Atomic and Splittable Flow, Price of Anarchy
2.7 Further Reading
2.8 Exercises for Chapter 2
3 Games in Strategic Form
3.1 Prerequisites and Learning Outcomes
3.2 Games in Strategic Form
3.3 Best Responses and Equilibrium
3.4 Games with Multiple Equilibria
3.5 Dominated Strategies
3.6 The Cournot Duopoly of Quantity Competition
3.7 Games without a Pure-Strategy Equilibrium
3.8 Symmetric Games with Two Strategies per Player
3.9 Further Reading
3.10 Exercises for Chapter 3
4 Game Trees with Perfect Information
4.1 Prerequisites and Learning Outcomes
4.2 Definition of Game Trees
4.3 Backward Induction
4.4 Strategies in Game Trees
4.5 Reduced Strategies
4.6 Subgame-Perfect Equilibrium (SPE)
4.7 Commitment Games
4.8 Further Reading
4.9 Exercises for Chapter 4
5 Expected Utility
5.1 Prerequisites and Learning Outcomes
5.2 Summary
5.3 Decisions Under Risk
5.4 Preferences for Lotteries
5.5 Ordinal Preferences for Decisions Under Certainty
5.6 Cardinal Utility Functions and Simple Lotteries
5.7 Consistency Axioms
5.8 Existence of an Expected-Utility Function
5.9 Risk Aversion
5.10 Discussion and Further Reading
5.11 Exercises for Chapter 5
6 Mixed Equilibrium
6.1 Prerequisites and Learning Objectives
6.2 Compliance Inspections
6.3 Bimatrix Games
6.4 The Best-Response Condition
6.5 Existence of Mixed Equilibria
6.6 Finding Mixed Equilibria in Small Games
6.7 The Upper-Envelope Method
6.8 Degenerate Games
6.9 Further Reading
6.10 Exercises for Chapter 6
7 Brouwer’s Fixed-Point Theorem
7.1 Prerequisites and Learning Outcomes
7.2 Labels
7.3 Simplices and Triangulations
7.4 Sperner’s Lemma
7.5 The Knaster–Kuratowski–Mazurkiewicz Lemma
7.6 Brouwer’s Fixed-Point Theorem on a General Compact Convex Set
7.7 The Freudenthal Triangulation
7.8 Further Reading
7.9 Exercises for Chapter 7
8 Zero-Sum Games
8.1 Prerequisites and Learning Outcomes
8.2 Example: Soccer Penalty
8.3 Max-Min and Min-Max Strategies
8.4 A Short Proof of the Minimax Theorem
8.5 Further Notes on Zero-Sum Games
8.6 Further Reading
8.7 Exercises for Chapter 8
9 Geometry of Equilibria in Bimatrix Games
9.1 Prerequisites and Learning Outcomes
9.2 Labeled Best-Response Regions
9.3 The Lemke–Howson Algorithm
9.4 Using Best-Response Diagrams
9.5 Strategic Equivalence
9.6 Best-Response Polyhedra and Polytopes
9.7 Complementary Pivoting
9.8 Degeneracy Resolution
9.9 Further Reading
9.10 Exercises for Chapter 9
10 Game Trees with Imperfect Information
10.1 Prerequisites and Learning Outcomes
10.2 Information Sets
10.3 Extensive Games
10.4 Strategies for Extensive Games and the Strategic Form
10.5 Reduced Strategies
10.6 Perfect Recall
10.7 Behavior Strategies
10.8 Kuhn’s Theorem: Behavior Strategies Suffice
10.9 Behavior Strategies in the Monty Hall Problem
10.10 Subgames and Subgame-Perfect Equilibria
10.11 Further Reading
10.12 Exercises for Chapter 10
11 Bargaining
11.1 Prerequisites and Learning Outcomes
11.2 Bargaining Sets
11.3 Bargaining Axioms
11.4 The Nash Bargaining Solution
11.5 Geometry of the Bargaining Solution
11.6 Splitting a Unit Pie
11.7 The Ultimatum Game
11.8 Alternating Offers Over Two Rounds
11.9 Alternating Offers Over Several Rounds
11.10 Stationary Strategies
11.11 The Nash Bargaining Solution Via Alternating Offers
11.12 Further Reading
11.13 Exercises for Chapter 11
12 Correlated Equilibrium
12.1 Prerequisites and Learning Outcomes
12.2 Examples of Correlated Equilibria
12.3 Incentive Constraints
12.4 Coarse Correlated Equilibrium
12.5 Existence of a Correlated Equilibrium
12.6 Further Reading
12.7 Exercises for Chapter 12
References
Index