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Introduction

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Disclaimer

I do not take any responsability about the correctness of this document. The following was put together to help myself while studying for the course. As such it was not intended to be shared and it may contain errors.

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Chapter index

  1. Games in strategic form: Non-cooperative Nash model

  2. Zero sum games

  3. Extensive form games

  4. Cooperative games

  5. Mechanism design, social choices

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Note about the exam (21/22 winter session)

The exam is divided in two parts, taken the same day:

  • 1/2 hour, closed book, multiple answer quiz with theoretical questions (24 points)

  • 1 hour, open book, two exercises like the ones seen in class (12 points)

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Exercise sessions schedule recap

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Week 1

  • Modeling a situation as a strategic game

    Common game theory problems, such as the prisoner dilemma or the el farol bar.

  • Nash equilibrium in strategic form games

    N.E. in pure strategies, find how the N.E. equilibria vary basing on the parameters.

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Week 2

  • Potential games

    Identify a game as a potential game, find the potential or identify parameters such that a game admits a potential.

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Week 3

  • Equilibria in mixed strategies for strategic form games

    Find parameters such that the strategy of a specific player given by the exercise text belongs to a N.E., or simply find the equilibria in mixed strategy:

  • Zero sum games

    Find equilibria via mix/max and max/min.

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Week 4

  • Zero sum games

    Find the optimal strategies and the value of the game.

  • Fair games

    Prove that the game is a fair game, find all the N.E.

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Week 5

  • Extensive form games

    Give an example of an extensive form games that respects some constraints, enumerate strategies, write the game in strategic form, apply backward induction to find N.E. Do the same but with parameters in the tree.

  • Combinatorial games

    Find which player is going to win, identify P-positions and N-positions. Find the probability of obtaining a P-position. Find how long is the rational play, Chomp game.

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Week 6

  • Cooperative games

    Find the core of the game, find if the game is super-additive. Check if the core of the game is empty.

    • TU games (transferable utility games)

      Find the Shapley and the Banzhaf values, find the nucleus.

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Week 7

  • Mechanism design

  • Social choice

NextChapter 1: Games in Strategic Form (Non cooperative Nash model)

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