Introduction to Game Theory Review for the Midterm Exam Dana Nau - - PowerPoint PPT Presentation

introduction to game theory review for the midterm exam
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Introduction to Game Theory Review for the Midterm Exam Dana Nau - - PowerPoint PPT Presentation

Introduction to Game Theory Review for the Midterm Exam Dana Nau University of Maryland Updated 10/14/10 Nau: Game Theory 1 Part 1 Basic concepts: normal form, utilities/payoffs, pure strategies, mixed strategies How utilities


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SLIDE 1

Nau: Game Theory 1 Updated 10/14/10

Introduction to Game Theory

Review for the Midterm Exam

Dana Nau University of Maryland

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SLIDE 2

Nau: Game Theory 2 Updated 10/14/10

Part 1

 Basic concepts:

  • normal form, utilities/payoffs, pure strategies, mixed strategies

 How utilities relate to rational preferences (not in the book)  Some classifications of games based on their payoffs

  • Zero-sum
  • Roshambo, Matching Pennies
  • Non-zero-sum
  • Chocolate Dilemma, Prisoner’s Dilemma, Battle of the Sexes,

Which Side of the Road?

  • Common-payoff
  • Which Side of the Road?
  • Symmetric
  • all of the above except Battle of the Sexes
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SLIDE 3

Nau: Game Theory 3 Updated 10/14/10

Part 2

 I’ve discussed several solution concepts, and ways of finding them:

  • Pareto optimality
  • Prisoner’s Dilemma, Which Side of the Road
  • best responses and Nash equilibria
  • Battle of the Sexes, Matching Pennies
  • finding Nash equilibria
  • real-world examples
  • soccer penalty kicks
  • road networks (Braess’s Paradox)
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SLIDE 4

Nau: Game Theory 4 Updated 10/14/10

Part 3

 maximin and minimax strategies, and the Minimax Theorem

  • Matching Pennies, Two-Finger Morra

 dominant strategies

  • Prisoner’s Dilemma, Which Side of the Road, Matching Pennies
  • Elimination of dominated strategies

 rationalizability

  • the p-Beauty Contest

 correlated equilibrium

  • Battle of the Sexes

 trembling-hand perfect equilibria  epsilon-Nash equilibria  evolutionarily stable strategies

  • Hawk-Dove game
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SLIDE 5

Nau: Game Theory 5 Updated 10/14/10

Part 4a

 Extensive-form games

  • relation to normal-form games
  • Nash equilibria
  • subgame-perfect equilibria
  • backward induction
  • The Centipede Game
  • backward induction in constant-sum games
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SLIDE 6

Nau: Game Theory 6 Updated 10/14/10

Part 4b

 If a game is two-player zero-sum, maximin and minimax are the same  If the game also is perfect-information, only need to look at pure strategies  If the game also is sequential, deterministic, and finite

  • minimax game-tree search - minimax values, alpha-beta pruning

 In sufficiently complicated games, perfection is unattainable

  • must approximate: limited search depth, static evaluation function

 In games that are even more complicated, further approximation is needed

  • Monte Carlo roll-outs
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SLIDE 7

Nau: Game Theory 7 Updated 10/14/10

Part 4c

 In most game trees

  • Increasing the search depth usually improves the decision-making

 In pathological game trees

  • Increasing the search depth usually degrades the decision-making

 Pathology is more likely when

  • The branching factor is high
  • The number of possible payoffs is small
  • Local similarity is low

 Even in ordinary non-pathological game trees, local pathologies can occur

  • Some research has been done on algorithms to detect and overcome

local pathologies, but it’s rather limited