CS344M Autonomous Multiagent Systems Patrick MacAlpine Department - - PowerPoint PPT Presentation

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CS344M Autonomous Multiagent Systems Patrick MacAlpine Department - - PowerPoint PPT Presentation

Jun 27, 2023 129 likes •445 views

CS344M Autonomous Multiagent Systems Patrick MacAlpine Department of Computer Science The University of Texas at Austin Good Afternoon, Colleagues Are there any questions? Patrick MacAlpine Logistics Progress reports due in 1 week

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SLIDE 1

CS344M Autonomous Multiagent Systems

Patrick MacAlpine Department of Computer Science The University of Texas at Austin

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SLIDE 2

Good Afternoon, Colleagues

Are there any questions?

Patrick MacAlpine

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SLIDE 3

Logistics

  • Progress reports due in 1 week

Patrick MacAlpine

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SLIDE 4

Logistics

  • Progress reports due in 1 week
  • Topic change for next week: multiagent learning

Patrick MacAlpine

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SLIDE 5

Logistics

  • Progress reports due in 1 week
  • Topic change for next week: multiagent learning
  • Talks in the department:

− FAI Talk - Sergey Levine, Frdiay 11am GDC 6.302

Patrick MacAlpine

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SLIDE 6

Mixed strategy equilibrium

P❧❛②❡r ✷ ❆❝t✐♦♥ ✶ ❆❝t✐♦♥ ✷ ❆❝t✐♦♥ ✶ ✸✱✼ ✷✱✷ P❧❛②❡r ✶ ❆❝t✐♦♥ ✷ ✻✱✺ ✶✱✼

Patrick MacAlpine

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SLIDE 7

Mixed strategy equilibrium

P❧❛②❡r ✷ ❆❝t✐♦♥ ✶ ❆❝t✐♦♥ ✷ ❆❝t✐♦♥ ✶ ✸✱✼ ✷✱✷ P❧❛②❡r ✶ ❆❝t✐♦♥ ✷ ✻✱✺ ✶✱✼

  • What if player 2 picks action 1 3/4 of the time?
  • What if player 2 picks action 1 1/4 of the time?
  • Player 1 must be indifferent between actions 1 and 2
  • Player 2 must be indifferent between actions 1 and 2

Patrick MacAlpine

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SLIDE 8

Correlated Equilibria

Patrick MacAlpine

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SLIDE 9

Correlated Equilibria

Sometimes mixing isn’t enough: Bach/Stravinsky

❲✐❢❡ ❙ ❇ ❙ ✷✱✶ ✵✱✵ ▼❡ ❇ ✵✱✵ ✶✱✷

Want only S,S or B,B - 50% each

Patrick MacAlpine

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SLIDE 10

Focal points

  • We will both be in Paris for some time in June.
  • We both know that we will both be there on the 15th.

Patrick MacAlpine

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SLIDE 11

Focal points

  • We will both be in Paris for some time in June.
  • We both know that we will both be there on the 15th.
  • Something happens so that we must meet on that day
  • We have no way of getting in touch.

Patrick MacAlpine

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SLIDE 12

Focal points

  • We will both be in Paris for some time in June.
  • We both know that we will both be there on the 15th.
  • Something happens so that we must meet on that day
  • We have no way of getting in touch.
  • When and where?

Patrick MacAlpine

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SLIDE 13

Focal points

  • We will both be in Paris for some time in June.
  • We both know that we will both be there on the 15th.
  • Something happens so that we must meet on that day
  • We have no way of getting in touch.
  • When and where?
  • What are the Nash equilibria?

Patrick MacAlpine

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SLIDE 14

Incomplete Information Games

  • We each get one of 3 cards: 1,2,3
  • If we both fold, we both lose nothing
  • If one raises and one folds, the raiser gets 1
  • If both raise, the one with the higher card gets 5
  • Zero sum

Patrick MacAlpine

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SLIDE 15

Incomplete Information Games

  • We each get one of 3 cards: 1,2,3
  • If we both fold, we both lose nothing
  • If one raises and one folds, the raiser gets 1
  • If both raise, the one with the higher card gets 5
  • Zero sum

❈❛r❞ ❄ ❘ ❋ ❘ ✺✱✲✺ ✶✱✲✶ ❈❛r❞ ✸ ❋ ✲✶✱✶ ✵✱✵

Patrick MacAlpine

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SLIDE 16

Incomplete Information Games

❈❛r❞ ❄ ❘ ❋ ❘ ✺✱✲✺ ✶✱✲✶ ❈❛r❞ ✸ ❋ ✲✶✱✶ ✵✱✵

Patrick MacAlpine

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SLIDE 17

Incomplete Information Games

❈❛r❞ ❄ ❘ ❋ ❘ ✺✱✲✺ ✶✱✲✶ ❈❛r❞ ✸ ❋ ✲✶✱✶ ✵✱✵ ❈❛r❞ ❄ ❘ ❋ ❘ ✲✺✱✺ ✶✱✲✶ ❈❛r❞ ✶ ❋ ✲✶✱✶ ✵✱✵

Patrick MacAlpine

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SLIDE 18

Bayes-Nash Equilibrium

  • 3 ⇒ raise

Patrick MacAlpine

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SLIDE 19

Bayes-Nash Equilibrium

  • 3 ⇒ raise
  • 1 ⇒ fold (no matter what the other one does with 2)

Patrick MacAlpine

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SLIDE 20

Bayes-Nash Equilibrium

  • 3 ⇒ raise
  • 1 ⇒ fold (no matter what the other one does with 2)
  • 2 ⇒ ?

Patrick MacAlpine

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SLIDE 21

Bayes-Nash Equilibrium

  • 3 ⇒ raise
  • 1 ⇒ fold (no matter what the other one does with 2)
  • 2 ⇒ ?

− Raise: (.5)(-5) + (.5)(1) = -2 − Fold: (.5)(-1) + (.5)(0) = -.5

Patrick MacAlpine

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SLIDE 22

Bayes-Nash Equilibrium

  • 3 ⇒ raise
  • 1 ⇒ fold (no matter what the other one does with 2)
  • 2 ⇒ ?

− Raise: (.5)(-5) + (.5)(1) = -2 − Fold: (.5)(-1) + (.5)(0) = -.5 − Always fold!

Patrick MacAlpine

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SLIDE 23

Bayes-Nash Equilibrium

  • 3 ⇒ raise
  • 1 ⇒ fold (no matter what the other one does with 2)
  • 2 ⇒ ?

− Raise: (.5)(-5) + (.5)(1) = -2 − Fold: (.5)(-1) + (.5)(0) = -.5 − Always fold! − Bayes-Nash: both players Raise if 3, otherwise Fold

Patrick MacAlpine

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SLIDE 24

Bayes-Nash Equilibrium

  • 3 ⇒ raise
  • 1 ⇒ fold (no matter what the other one does with 2)
  • 2 ⇒ ?

− Raise: (.5)(-5) + (.5)(1) = -2 − Fold: (.5)(-1) + (.5)(0) = -.5 − Always fold! − Bayes-Nash: both players Raise if 3, otherwise Fold With more numbers and/or different payoffs, bluffing can be a part of the Nash Equilibrium

Patrick MacAlpine

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SLIDE 25

Discussion

  • How useful is the concept of Nash equilibrium?

Patrick MacAlpine

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SLIDE 26

Discussion

  • How useful is the concept of Nash equilibrium?
  • What if one player isn’t rational?

Patrick MacAlpine

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SLIDE 27

Discussion

  • How useful is the concept of Nash equilibrium?
  • What if one player isn’t rational?
  • What can’t game theory simulate?

Patrick MacAlpine

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SLIDE 28

Repeated games

  • Book slides

Patrick MacAlpine

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SLIDE 29

Repeated games

  • Book slides
  • Tournaments on resources page

Patrick MacAlpine

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Repeated games

  • Book slides
  • Tournaments on resources page
  • Threats slides

Patrick MacAlpine

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SLIDE 31

Repeated games

  • Book slides
  • Tournaments on resources page
  • Threats slides
  • Doran’s ICML slides

Patrick MacAlpine