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Advanced Artificial Intelligence

Advanced Artificial Intelligence. Lecture 3B: Game theory. Outline. Decisions with multiple agents: game theory(Text book: 17.5 ) . Game Theory. For games where two players move simultaneously (or, without knowledge of each other) Often, single-move games Two problems are studied

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Advanced Artificial Intelligence

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  1. Advanced Artificial Intelligence Lecture 3B: Game theory

  2. Outline • Decisions with multiple agents: game theory(Text book: 17.5 ) 

  3. Game Theory • For games where two players move simultaneously (or, without knowledge of each other) • Often, single-move games • Two problems are studied • Agent design • Mechanism design

  4. Prisoner’s Dilemma • Dominant Strategy: testify(does better no matter what other player does) • Pareto Optimal: no other outcome that all players would prefer • Equilibrium: no player can benefit from switching (assuming other players stay the same)Every game has at least one (Nash)

  5. Game Console Game • Dominant Strategy? • No • Equilibrium? • blu,blu; dvd,dvd • Pareto Optimal? • Blu,blu: +9, +9

  6. Sample Game • Two finger Morra: players E and O show 1 or 2 fingers; total f. E wins f if even; O if odd. • What is best strategy for each player (solution)? • Pure strategy: single move • Mixed strategy: probability distribution on moves

  7. -3 ≤ UE ≤ 2

  8. - -1/12 ≤ UE ≤ -1/12

  9. Poker • Deck: KKAA • Deal: 1 card each • Rounds: • raise/check • call/fold • Sequential game; • Extensive form

  10. Convert to Normal Form Problem: number of strategies exponential in number of information sets Texas Hold’em: 1018 states.

  11. Extensive Games • Sequence form (Koller): Up to 25,000 states • Abstraction • Suits; Hi/mid/lo; bet amounts; only some deals • Can handle • PO, multi-agent, stochastic, sequential, dynamic • Can’t handle (very well) • Unknown actions; continuous actions • Irrational opponents • Unknown utilities

  12. Mechanism Design • Game Theory: • Given a game, find rational policy • Mechanism Design: • Given utility functions Ui, design a game such that the rational strategies maximize ∑ Ui • Examples: • Google ads, airplane tickets, radio spectra, TCP packets, dating, doctor internships

  13. Auction • Auction is globally better with more bidders • Easier if bidders have dominant strategy • Strategy-proof; truth-revealing; incentive compatible • Sealed bid auction • Strategy-proof? • Second-price (Vickrey) auction • Payoff for bid b with value v, best other bid c: U = (v – c) if (b > c) else 0 • Optimal bid: • Bid v

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