1 / 14

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

stephen-potts
Download Presentation

Advanced Artificial Intelligence

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related