Unit No | Topics |
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Introduction | What is Game Theory? Definition of Games. Actions, Strategies, Preferences, Payoffs. Examples; Strategic Form Games - Strategic form games and examples: Prisoner's Dilemma, Bach or Stravinsky, Matching Pennies, Tragedy of Commons, Braess Paradox |

Dominant Strategy Equilibrium | Strongly dominant strategies, weakly dominant strategies, dominant strategy equilibrium; Examples of Prisoner‟s Dilemma and Vickrey Auction |

Pure Strategy Nash Equilibrium | Best response strategies; Notion of pure strategy Nash equilibrium. Examples of Nash Equilibrium. Examples of Nash Equilibrium in popular games. Symmetric Games and Symmetric Equilibria; Mixed Strategy Nash Equilibrium- Randomization of Actions, Mixed strategy Nash equilibrium, Necessary and sufficient conditions for a Nash equilibrium. Examples of mixed strategy Nash equilibrium. Computing mixed strategy Nash equilibria. Related algorithmic issues |

Two Player Zero sum Games (Matrix Games) | Max-minimization and Minmaximization. Saddle points. Nash equilibrium in matrix games. Mini-max theorem. Solution via linear programming. Examples; Extensive games with Perfect Information-Extensive games, Strategies and outcomes, Nash equilibrium, Subgame perfect equilibrium, finding subgame perfect equilibria using backward induction. Allowing for simultaneous moves. Examples |

Bayesian Games | Motivational Examples. Definition of a Bayesian Game and Bayesian Nash Equilibrium and examples |

Mechanism Design | Social choice functions. Direct and indirect mechanisms. Notion of incentive compatibility. Revelation theorem. Properties of social choice functions. Gibbard Satterthwaite theorem. Quasi-linear utilities. Vickrey auction. Clarke mechanisms. Groves mechanisms. Examples of VCG (Vickrey-Clarke- Groves) mechanisms. Different types of auctions. Revenue equivalence theorem |

Cooperative Game Theory | Correlated strategies and correlated equilibrium. The two person Nash bargaining problem and its solution with examples. Games in characteristic form and examples. . The Core of a characteristic form game. Shapley value and its implications. Examples |

Attachment | Size |
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5th Game Theory.pdf | 239.46 KB |