CSC304 Lecture 22 CSC304 - Nisarg Shah 1 BUT FIRST Course - - PowerPoint PPT Presentation

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CSC304 Lecture 22 CSC304 - Nisarg Shah 1 BUT FIRST Course - - PowerPoint PPT Presentation

Dec 25, 2022 186 likes •322 views

CSC304 Lecture 22 CSC304 - Nisarg Shah 1 BUT FIRST Course Evaluation Low response rate CSC304 - Nisarg Shah 2 Complete your course evaluations Check your e-mail for a link to your evaluations, or log-in to www.portal.utoronto.ca and

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CSC304 Lecture 22

CSC304 - Nisarg Shah 1

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BUT FIRST…

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Course Evaluation Low response rate

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Complete your course evaluations…

Check your e-mail for a link to your evaluations, or log-in to www.portal.utoronto.ca and click the Course Evals tab!

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Should I expect drumrolls?

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Course Evaluation New response rate

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REVIEW (Of most concepts)

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Part I: Game Theory

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  • Normal (matrix) form games
  • Strategies: pure & mixed
  • Weak/strict dominance

➢ Strategy A dominates strategy B ➢ Iterated elimination of dominated strategy ➢ Strategy A is dominant

  • Nash equilibrium: pure and mixed

➢ Nash’s theorem

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Part I: Game Theory

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  • Price of anarchy and stability

➢ Anarchy: Worst NE vs social optimum ➢ Stability: Best NE vs social optimum ➢ PoA ≥ PoS ≥ 1

  • Potential functions

➢ Cost-sharing games ➢ Braess’ paradox

  • Zero-sum games

➢ The minimax theorem

  • Stackelberg games, Stackelberg equilibrium
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Part II: Mech Design w/ Money

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  • Goals: social welfare or revenue
  • Incentive guarantees:

➢ Strategyproofness ➢ Bayes-Nash incentive compatibility (BNIC)

  • VCG mechanism

➢ Strategyproof + maximizes social welfare on every instance ➢

𝑛 approximation for single-minded bidders

➢ Sponsored search, comparison to GSP

  • Myerson’s auction

➢ Strategyproof + maximizes expected revenue among all BNIC

mechanisms

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Part II: Mech Design w/ Money

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  • Revelation principle
  • Revenue equivalence principle
  • Bayes-Nash equilibria of non-BNIC mechanisms

➢ 1st price auction and its equilibrium

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Part III: Mech Design w/o Money

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  • Facility location
  • Social cost

➢ The median mechanism

  • Maximum cost

➢ The left-right-middle mechanism

  • Stable matching

➢ Gale-Shapley deferred acceptance algorithm

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Part IV: Voting

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  • Ranked voting
  • Voting rules
  • Gibbard-Satterthwaite theorem
  • Axiomatic approach to voting

➢ Strategyproofness, strong / weak monotonicity,

consistency, Condorcet consistency

  • Utilitarian approach to voting
  • Impartial selection
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Part V: Fair Division

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  • Cake-cutting

➢ Proportionality and envy-freeness ➢ Robertson-Webb model

  • 2-players

➢ Cut-and-choose

  • 3+ players proportional

➢ Dubins-Spanier protocol (moving knife) ➢ Even-Paz protocol

  • Pareto optimality
  • Strategyproofness via perfect partition
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Part V: Fair Division

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  • Indivisible goods

➢ Envy-freeness up to one good ➢ Maximum Nash Welfare allocation