What is included with this book?
Preface | p. vii |
Basic ideas | p. 1 |
Around the prisoner's dilemma | p. 3 |
What is a two-player game? | p. 3 |
Prisoner's dilemma. Dominated strategies and Pareto optimality | p. 7 |
Prisoner's dilemma for crooks, warriors and opera lovers | p. 9 |
Discrete duopoly models and common pool resources; public goods | p. 12 |
Common knowledge, rationality and iterated elimination of strictly dominated strategies | p. 13 |
Weak dominance; debtors and creditors | p. 15 |
Nash equilibrium | p. 16 |
Battle of the sexes and Kant's categorical imperative | p. 19 |
Chicken game and the Cuban missile crisis | p. 21 |
Social dilemmas | p. 22 |
Guaranteed payoff, minimax strategy, hedge | p. 25 |
Utility function | p. 26 |
General objectives of game theory; Pascal's wager | p. 27 |
Auctions and networks | p. 29 |
Several players; the volunteers' dilemma | p. 29 |
An example on iterated elimination of dominated strategies | p. 31 |
Second price and increasing bid auctions | p. 32 |
Escalating conflicts | p. 34 |
Braess paradox | p. 35 |
Wardrop equilibria and selfish routing | p. 37 |
Wise men and businessmen | p. 39 |
Wise men and their wives; imp in the bottle | p. 39 |
King Solomon's wisdom | p. 41 |
Chain store paradox; centipede game | p. 43 |
Normal and extensive forms of a game; battle of the sexes revisited | p. 46 |
Dynamic games and subgame perfection; pursuit games | p. 48 |
Fair division and the ultimatum game | p. 50 |
Cooperation by threat and punishment; infinitely repeated games | p. 51 |
Computer tournaments; the triumph of the strategy Tit-for-Tat | p. 58 |
Logical games; limits of the sequences | p. 59 |
Russian Roulette; games with incomplete information | p. 62 |
Hawk and doves, lions and lambs | p. 65 |
Fitness and stability in population biology (general ideas) | p. 65 |
Hawk and Dove games as social dilemmas | p. 67 |
Mixed strategies, probability and chance | p. 69 |
The theorems of Nash and von Neumann | p. 73 |
Expectation and risk; St. Petersburg game | p. 74 |
Symmetric mixed strategies Nash equilibria | p. 75 |
Invasion of mutants and evolutionary stable strategies | p. 77 |
The sex ratio game | p. 80 |
Coalitions and distribution | p. 81 |
Distribution of costs and gains; the core of the game | p. 81 |
General principles of fair distribution | p. 85 |
Utilitarianism and egalitarianism; compromise set | p. 88 |
Equilibrium priced | p. 91 |
Linear models and linear programming | p. 93 |
Presidents and dictators | p. 95 |
Collective choice; problems of voting | p. 95 |
Four examples of voting rules | p. 97 |
Criteria of quality of voting rules | p. 99 |
The minority principle; dictators | p. 102 |
At the doors of quantum games | p. 105 |
Quantum bits and Schrödinger's cat | p. 105 |
Lattices and quantum logic | p. 108 |
Rendezvous of Bob and Alice | p. 111 |
It's party time! | p. 113 |
Combinatorial games | p. 113 |
Addition and subtraction of games, order structure | p. 117 |
Impartial games and Nim numbers | p. 119 |
Games as numbers and numbers as games | p. 123 |
Armed with mathematics | p. 125 |
A rapid course in mathematical game theory | p. 127 |
Three classical examples of Nash equilibria in economics | p. 127 |
Mixed strategies for finite games | p. 131 |
Evolutionary stable strategies | p. 139 |
Replicator dynamics, Nash's fields and stability | p. 141 |
Iterative method of solving matrix games | p. 156 |
Zero-sum games and linear programming | p. 159 |
Backward induction and dynamic programming | p. 161 |
Cooperative games: Nucleus and the Shapley vector | p. 167 |
Revision exercises | p. 168 |
Solutions to revision exercises | p. 173 |
Examples of game models | p. 179 |
A static model of strategic investment | p. 179 |
Variations Cournot's theme: Territorial price building | p. 182 |
Models of inspection | p. 184 |
A dynamic model of strategic investments | p. 191 |
Game theoretic approach to the analysis of colored (or rainbow) options | p. 197 |
Elements of more advanced analysis | p. 211 |
Short overview | p. 211 |
Two proofs of the Nash-Gliksberg theorem on the existence of equilibria | p. 212 |
Introduction to structural stability | p. 216 |
Introduction to abstract differential games | p. 229 |
Cooperative games versus zero-sum games | p. 237 |
Turnpikes for stochastic games | p. 240 |
Games and tropical (or idempotent) mathematics | p. 245 |
The first order partial differential equations in multi-criteria optimization problems | p. 253 |
General flows of deterministic and stochastic replicator dynamics | p. 259 |
Bibliography | p. 273 |
Index | p. 283 |
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