Game Theory

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Game Theory Classes

Introduction

  • A Game Theory Based Predation Behavior 2008 Chen Shi
  • ingredients: players, strategies, payoffs
  • simple collection active game
  • team games -> ultimate competition

Dominance

  • Optimal Strategy to Solution Concepts
  • Decision theory, single theory

Nash Equilibrium

  • Cournot-Nash -- what pushes people towards equilibrium?
  • Nash equilibrium with many players. Keynes' Beauty Contest Game.
  • Braess' Paradox; traffic game
  • Tragedy of the Commons
  • Minimax Theorem
  • best response correspondences
  • finite number of pure strategies -> has at least one nash equilibrium
  • Palacios-Huerta & Volij (2009 American Economic Review)

Extensive Form Games

  • perfect vs. imperfect information (game tree)
  • game tree: root node, terminal nodes. Easy to understand but has cumbersome notation -- "a lot of notation to specify the obvious"
  • off path strategies
  • mixed strategies vs. behavioral strategies (Kuhn's Theorem) -- doesn't matter for perfect information
  • centipede game (R. McKelvey and T. Palfrey)
  • unique backward induction
  • entry game
  • different
  • information sets
  • subgame perfect equilibrium (include all children)

Repeated Games

  • Many interactions occur more than once
  • Tit-for-tat Axelrod prisoner's dilemma
  • finite: always defect, but people tend to play as if it was indefinite
  • the stage game
  • limit average rewards; future-discounted reward
  • grim trigger
  • P. Dal Bo American Economic Review vol 95, repeated
  • "Folk" Theorems

Bayesian Games and Auctions

Other

Observations

  • Game Theory: A Nontechnical Introduction by Morton D. Davis.
  • One-Person games are really a player against "nature". These games can be broken down into three categories.

Risk Aversion

I believe that there is asymmetry in winning versus losing positions.

  • "If you have nothing to lose, you can try everything" -- Yiddish Proverb

Generals

3:2

0:3  Win, Lose  2 (1/3) (33.3)
1:2  Win, Tie   3 (1/6) (16.7)
2:1  Win, Win   4 (1/6) (16.7)
3:0  Tie, Win   3 (1/3) (33.3)

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4:1

0:3 Win, Lose   2 (1/3) (33.3)
1:2 Win, Lose   2 (1/6) (16.7)
2:1 Win, Tie    3 (1/6) (16.7)
3:0 Win, Win    4 (1/3) (33.3)

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