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Full Description
We live in a highly connected world with multiple self-interested agents interacting and myriad opportunities for conflict and cooperation. The goal of game theory is to understand these opportunities.
This book presents a rigorous introduction to the mathematics of game theory without losing sight of the joy of the subject. This is done by focusing on theoretical highlights (e.g., at least six Nobel Prize winning results are developed from scratch) and by presenting exciting connections of game theory to other fields such as computer science (algorithmic game theory), economics (auctions and matching markets), social choice (voting theory), biology (signaling and evolutionary stability), and learning theory. Both classical topics, such as zero-sum games, and modern topics, such as sponsored search auctions, are covered. Along the way, beautiful mathematical tools used in game theory are introduced, including convexity, fixed-point theorems, and probabilistic arguments.
The book is appropriate for a first course in game theory at either the undergraduate or graduate level, whether in mathematics, economics, computer science, engineering, or statistics. The importance of game-theoretic thinking transcends the academic setting-for every action we take, we must consider not only its direct effects, but also how it influences the incentives of others.
Contents
Analyzing games: Strategies and equilibria: Combinatorial games
Two-person zero-sum games
Zero-sum games on graphs
General-sum games
Existence of Nash equilibria and fixed points
Games in existensive form
Evolutionary and correlated equilibria
The price of anarchy
Random-turn games
Designing games and mechanisms: Stable matching and allocation
Fair division
Cooperative games
Social choice and voting
Auctions
Truthful auction in win/lose settings
VCG and scoring rules
Matching markets
Adaptive decision making
Linear programming
Some useful probability toolds
Convex functions
Solution sketches for selected exercises
Bibliography
Index
