Coordinate Systems for Games: Simplifying the "me" and "we" Interactions (Static & Dynamic Game Theory: Foundations & Applications)

Preface
	Book Outline
Contents
1 Introduction
	1.1 Review
	1.2 An Inherent Dynamic
		1.2.1 Nash Dynamics
		1.2.2 Structure of 2times2 Games
	1.3 Standard Games
		1.3.1 Games with One Nash Cell
		1.3.2 Games with Two Nash Cells
	1.4 Mixed Strategies
		1.4.1 Games Without Nash Cells
		1.4.2 Finding the Probabilities
		1.4.3 Matching Pennies
		1.4.4 Another Source of Mixed Strategies
	1.5 Nash Theorem and Defining Generic and Degenerate Settings
2 Two-Player, Two-Strategy Games
	2.1 Preview
	2.2 Introduction
	2.3 The Nash Decomposition
		2.3.1 The Nash, or ``me\'\' Component
		2.3.2 The Behavioral ``we\'\' Factor, and Kernel Terms
		2.3.3 More Examples
	2.4 Gaining Intuition; Comparing Examples
		2.4.1 The Nash Component and Game Dynamic
		2.4.2 Behavior Component and Cooperation
		2.4.3 What Does All of This Mean?
		2.4.4 Creating Exotic Examples
		2.4.5 Does Size Matter?
	2.5 Structure of Standard Games
		2.5.1 Prisoner\'s Dilemma
		2.5.2 Collective Action
		2.5.3 Cooperation
		2.5.4 Hawk–Dove
		2.5.5 Battle of the Sexes
		2.5.6 Stag Hunt
	2.6 Risk Versus Payoff Dominance
		2.6.1 Payoff Dominance
		2.6.2 Risk Dominance
		2.6.3 Examples
		2.6.4 A 50–50 Choice
	2.7 Recap
3 Consequences
	3.1 Introduction
	3.2 Symmetric Games
	3.3 Zero-Sum and Identical Play
		3.3.1 CoCo Solutions
		3.3.2 Zero-Sum Games
		3.3.3 Identical Play Games
	3.4 Using Vectors to Analyze and Design Games
		3.4.1 Review of Vector Analysis
		3.4.2 Intuition and a Vector Basis
		3.4.3 Designing Games
		3.4.4 Utility Functions
		3.4.5 Congestion and Potential Games
		3.4.6 Zero-Sum, Identical Play Games
	3.5 Missing Terms When Analyzing Beliefs
	3.6 Roadmap of 2times2 Games
		3.6.1 The Nash Portion Is a Square; Ok, A Torus
		3.6.2 Likelihood of Different Strategic Structures
		3.6.3 Extending a Monderer–Shapley Observation
		3.6.4 Why Not Symmetric, Antisymmetric?
	3.7 The Behavioral Portion and a Circle
4 Two-Person Multi-strategy Games
	4.1 Introduction
	4.2 Decomposition
		4.2.1 More on Risk and Payoff Dominance
		4.2.2 More on Zero-Sum and Identical Play Games
	4.3 Examples
		4.3.1 Ultimatum Game
		4.3.2 Legislator Pay Raise Game
	4.4 Modeling and Creating Games
		4.4.1 Differences in the mathcalGB Structure
		4.4.2 Dimension Counting
	4.5 Structure of Two-Person Games
		4.5.1 Where\'s Waldo?
		4.5.2 Next Response Dynamic
	4.6 Structure of the Next Response Dynamic
		4.6.1 Number of Hyperbolic Cells
		4.6.2 The Next Response Dynamic
	4.7 Some Games
		4.7.1 Colonel Blotto
		4.7.2 Rock-Paper-Scissors
		4.7.3 Those Repulsive Cells
	4.8 Computing Mixed Equilibria
		4.8.1 Help from the Decomposition
		4.8.2 Moving to 3times3 Blocks
5 Extensive Form Games
	5.1 What Is with What?
	5.2 Centipede Game
	5.3 Equilibria and Subgame Equilibrium
	5.4 Nature\'s Involvement in a 2times2 Game
	5.5 From a Decomposition to Coordinates
		5.5.1 Nash Component for the General Game
		5.5.2 Changing Probabilities
		5.5.3 The Behavioral Terms for the General Game
	5.6 Paradise for Designers!
	5.7 Details of the Decomposition
		5.7.1 Subgames and Decisions
		5.7.2 Player 2
		5.7.3 Player 1
		5.7.4 Alternative Basis for Behavioral Coordinates
6 Multiplayer Games
	6.1 Hawk–Dove–Dove
		6.1.1 Analyzing Hawk–Dove–Dove
		6.1.2 Designing a Hawk–Dove–Dove Game
	6.2 Nash Dynamic Structure
		6.2.1 Adding Complexity
		6.2.2 Those Retaliatory Strategies
	6.3 New Symmetries
		6.3.1 A Wedding Between Voting and Game Theory
		6.3.2 Another Designer\'s Delight! Coalition-Free Nash Points?
		6.3.3 More Strategies, More Cycles
	6.4 Comments
7 The Underlying Mathematics
	7.1 Decompositions
	7.2 Definitions
	7.3 Symmetry
	7.4 Algebraic Structure of Games
		7.4.1 Symmetries of the Space of Games
		7.4.2 Homomorphisms
		7.4.3 Module
	7.5 Best Response Algebraic Structures
	7.6 Decompositions of Games
	7.7 Finding the Structure
		7.7.1 Conjugacy Classes
		7.7.2 Nash Decomposition
		7.7.3 Row-and-Column Decomposition–Potential Games
		7.7.4 Pareto Decomposition–CoCo Solutions
	7.8 Conclusion
8 Summary
Appendix  References
Index