CS344M Autonomous Multiagent Systems Todd Hester Department of - - PowerPoint PPT Presentation

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CS344M Autonomous Multiagent Systems Todd Hester Department of - - PowerPoint PPT Presentation

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CS344M Autonomous Multiagent Systems Todd Hester Department of Computer Science The University of Texas at Austin Good Afternoon, Colleagues Are there any questions? Todd Hester Logistics Progress reports due at beginning of class 2

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SLIDE 1

CS344M Autonomous Multiagent Systems

Todd Hester Department of Computer Science The University of Texas at Austin

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SLIDE 2

Good Afternoon, Colleagues

Are there any questions?

Todd Hester

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SLIDE 3

Logistics

  • Progress reports due at beginning of class

− 2 hard copies − Attach your proposals − Anonymized soft copy

Todd Hester

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SLIDE 4

Logistics

  • Progress reports due at beginning of class

− 2 hard copies − Attach your proposals − Anonymized soft copy

  • Peer reviews due next Thursday

Todd Hester

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SLIDE 5

Logistics

  • Progress reports due at beginning of class

− 2 hard copies − Attach your proposals − Anonymized soft copy

  • Peer reviews due next Thursday
  • Prof. Stone will teach class Thursday

Todd Hester

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SLIDE 6

Distributed Rational Decision Making

Self-interested, rational agent

Todd Hester

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SLIDE 7

Distributed Rational Decision Making

Self-interested, rational agent

  • Self-interested:

Todd Hester

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SLIDE 8

Distributed Rational Decision Making

Self-interested, rational agent

  • Self-interested: maximize own goals

– No concern for global good

Todd Hester

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SLIDE 9

Distributed Rational Decision Making

Self-interested, rational agent

  • Self-interested: maximize own goals

– No concern for global good

  • Rational:

Todd Hester

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SLIDE 10

Distributed Rational Decision Making

Self-interested, rational agent

  • Self-interested: maximize own goals

– No concern for global good

  • Rational: agents are smart

– Ideally, will act optimally

Todd Hester

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SLIDE 11

Distributed Rational Decision Making

Self-interested, rational agent

  • Self-interested: maximize own goals

– No concern for global good

  • Rational: agents are smart

– Ideally, will act optimally The protocol is key

Todd Hester

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SLIDE 12

Evaluation Criteria

  • Social welfare
  • Pareto efficiency
  • Stability

Todd Hester

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SLIDE 13

Evaluation Criteria

  • Social welfare
  • Pareto efficiency
  • Stability
  • Individual Rationality

Todd Hester

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SLIDE 14

Evaluation Criteria

  • Social welfare
  • Pareto efficiency
  • Stability
  • Individual Rationality
  • Efficiency (computational, communication)

Todd Hester

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SLIDE 15

Voting vs. auctions

  • Voting: maximize social good

– result affects all

Todd Hester

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SLIDE 16

Voting vs. auctions

  • Voting: maximize social good

– result affects all

  • Auctions: maximize profit

– result affects buyer and seller

Todd Hester

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SLIDE 17

Activity

  • Pick an integer between 1 and 20, write it down

Todd Hester

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SLIDE 18

Activity

  • Pick an integer between 1 and 20, write it down
  • Draw a line under it
  • Pick another number, write it under the line.

Todd Hester

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SLIDE 19

Activity

  • Pick an integer between 1 and 20, write it down
  • Draw a line under it
  • Pick another number, write it under the line.
  • 1st price sealed-bid auction

Todd Hester

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SLIDE 20

Activity

  • Pick an integer between 1 and 20, write it down
  • Draw a line under it
  • Pick another number, write it under the line.
  • 1st price sealed-bid auction
  • The top number is your utility

Todd Hester

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SLIDE 21

Activity

  • Pick an integer between 1 and 20, write it down
  • Draw a line under it
  • Pick another number, write it under the line.
  • 1st price sealed-bid auction
  • The top number is your utility
  • Goal: as much profit as possible

Todd Hester

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SLIDE 22

Activity

  • Pick an integer between 1 and 20, write it down
  • Draw a line under it
  • Pick another number, write it under the line.
  • 1st price sealed-bid auction
  • The top number is your utility
  • Goal: as much profit as possible
  • Write down your bid

Todd Hester

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SLIDE 23

Activity

  • Pick an integer between 1 and 20, write it down
  • Draw a line under it
  • Pick another number, write it under the line.
  • 1st price sealed-bid auction
  • The top number is your utility
  • Goal: as much profit as possible
  • Write down your bid
  • Repeat with 2nd price sealed-bid auction
  • Number under the line is your utility

Todd Hester

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SLIDE 24

Auctions

  • Valuations:

Todd Hester

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SLIDE 25

Auctions

  • Valuations:

− private value

Todd Hester

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SLIDE 26

Auctions

  • Valuations:

− private value − common value

Todd Hester

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SLIDE 27

Auctions

  • Valuations:

− private value − common value − correlated value

Todd Hester

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SLIDE 28

Auctions

  • Valuations:

− private value − common value − correlated value

  • Types:

− first-price open-cry (English)

Todd Hester

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SLIDE 29

Auctions

  • Valuations:

− private value − common value − correlated value

  • Types:

− first-price open-cry (English) − first-price sealed-bid

Todd Hester

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SLIDE 30

Auctions

  • Valuations:

− private value − common value − correlated value

  • Types:

− first-price open-cry (English) − first-price sealed-bid − descending (Dutch)

Todd Hester

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SLIDE 31

Auctions

  • Valuations:

− private value − common value − correlated value

  • Types:

− first-price open-cry (English) − first-price sealed-bid − descending (Dutch) − second-price sealed-bid (Vickrey)

Todd Hester

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SLIDE 32

Auctions

  • Valuations:

− private value − common value − correlated value

  • Types:

− first-price open-cry (English) − first-price sealed-bid − descending (Dutch) − second-price sealed-bid (Vickrey) Revenue equivalence: private-value, risk-neutral

Todd Hester

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SLIDE 33

Auctions

  • You value a bunch of flowers at $100

Todd Hester

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SLIDE 34

Auctions

  • You value a bunch of flowers at $100
  • What strategy if auction is:

– English

Todd Hester

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Auctions

  • You value a bunch of flowers at $100
  • What strategy if auction is:

– English – first-price sealed-bid

Todd Hester

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SLIDE 36

Auctions

  • You value a bunch of flowers at $100
  • What strategy if auction is:

– English – first-price sealed-bid – Descending

Todd Hester

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SLIDE 37

Auctions

  • You value a bunch of flowers at $100
  • What strategy if auction is:

– English – first-price sealed-bid – Descending – Vickrey

Todd Hester

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SLIDE 38

Auctions

  • You value a bunch of flowers at $100
  • What strategy if auction is:

– English – first-price sealed-bid – Descending – Vickrey

  • What if it’s an antique?

Todd Hester

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SLIDE 39

Auctions

  • Vickrey, English are truthful

Todd Hester

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SLIDE 40

Auctions

  • Vickrey, English are truthful
  • First-price sealed-bid: bidders bid lower than values

Todd Hester

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SLIDE 41

Auctions

  • Vickrey, English are truthful
  • First-price sealed-bid: bidders bid lower than values

– Private value case: why?

Todd Hester

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SLIDE 42

Auctions

  • Vickrey, English are truthful
  • First-price sealed-bid: bidders bid lower than values

– Private value case: why?

  • In common (and correlated) value case, bids lower in all

mechanisms

Todd Hester

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SLIDE 43

Auctions

  • Vickrey, English are truthful
  • First-price sealed-bid: bidders bid lower than values

– Private value case: why?

  • In common (and correlated) value case, bids lower in all

mechanisms – Why?

Todd Hester

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SLIDE 44

Auctions

  • Vickrey, English are truthful
  • First-price sealed-bid: bidders bid lower than values

– Private value case: why?

  • In common (and correlated) value case, bids lower in all

mechanisms – Why? Winner’s curse

Todd Hester

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SLIDE 45

Auctions

  • How could you collude?

Todd Hester

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SLIDE 46

Auctions

  • How could you collude?

– English

Todd Hester

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SLIDE 47

Auctions

  • How could you collude?

– English – first-price sealed-bid

Todd Hester

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SLIDE 48

Auctions

  • How could you collude?

– English – first-price sealed-bid – Descending

Todd Hester

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SLIDE 49

Auctions

  • How could you collude?

– English – first-price sealed-bid – Descending – Vickrey

Todd Hester

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SLIDE 50

Auctions

  • How could you collude?

– English – first-price sealed-bid – Descending – Vickrey

  • Incentive to break coalition?

Todd Hester

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SLIDE 51

Auctions

  • How could you collude?

– English – first-price sealed-bid – Descending – Vickrey

  • Incentive to break coalition?
  • Does everyone need to be in collusion?

Todd Hester

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SLIDE 52

Auctions

  • How could you collude?

– English – first-price sealed-bid – Descending – Vickrey

  • Incentive to break coalition?
  • Does everyone need to be in collusion?
  • Application of auctions to robot soccer?

Todd Hester

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SLIDE 53

Auctions vs. voting

  • Auctions: maximize profit

– result affects buyer and seller

  • Voting: maximize social good

– result affects all

Todd Hester

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SLIDE 54

Gibbard-Satterthwaite

  • Example: Bush, Gore, or Nader?

Todd Hester

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Gibbard-Satterthwaite

  • Example: Bush, Gore, or Nader?

– Assume your preference is Nader > Gore > Bush – For whom should you vote?

Todd Hester

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SLIDE 56

Gibbard-Satterthwaite

  • Example: Bush, Gore, or Nader?

– Assume your preference is Nader > Gore > Bush – For whom should you vote? – What if we change the system?

Todd Hester

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SLIDE 57

Gibbard-Satterthwaite

  • Example: Bush, Gore, or Nader?

– Assume your preference is Nader > Gore > Bush – For whom should you vote? – What if we change the system? – Plurality, Binary, Borda?

Todd Hester

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SLIDE 58

Gibbard-Satterthwaite

  • Example: Bush, Gore, or Nader?

– Assume your preference is Nader > Gore > Bush – For whom should you vote? – What if we change the system? – Plurality, Binary, Borda?

  • 3+ candidates =

⇒ only dictatorial system eliminates need for tactical voting − One person appointed

Todd Hester

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SLIDE 59

Gibbard-Satterthwaite

  • Example: Bush, Gore, or Nader?

– Assume your preference is Nader > Gore > Bush – For whom should you vote? – What if we change the system? – Plurality, Binary, Borda?

  • 3+ candidates =

⇒ only dictatorial system eliminates need for tactical voting − One person appointed

  • No point thinking of a “better” voting system
  • Assumption: no restrictions on preferences

Todd Hester

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SLIDE 60

Gibbard-Satterthwaite

  • Example: Bush, Gore, or Nader?

– Assume your preference is Nader > Gore > Bush – For whom should you vote? – What if we change the system? – Plurality, Binary, Borda?

  • 3+ candidates =

⇒ only dictatorial system eliminates need for tactical voting − One person appointed

  • No point thinking of a “better” voting system
  • Assumption: no restrictions on preferences

What about Clarke tax algorithm?

Todd Hester

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SLIDE 61

Types of Tactical Voting

  • Compromising:

Rank someone higher to get him/her elected − e.g. Gore instead of Nader

Todd Hester

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SLIDE 62

Types of Tactical Voting

  • Compromising:

Rank someone higher to get him/her elected − e.g. Gore instead of Nader

  • Burying: Rank someone lower to get him/her defeated

− e.g. in Borda protocol

Todd Hester

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SLIDE 63

Types of Tactical Voting

  • Compromising:

Rank someone higher to get him/her elected − e.g. Gore instead of Nader

  • Burying: Rank someone lower to get him/her defeated

− e.g. in Borda protocol

  • Push-over: Rank someone higher to get someone else

elected − e.g. in a protocol with multiple rounds

Todd Hester

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SLIDE 64

Arrow’s Theorem

Universality.

Todd Hester

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SLIDE 65

Arrow’s Theorem

  • Universality. The voting method should provide a complete

ranking of all alternatives from any set of individual preference ballots.

Todd Hester

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SLIDE 66

Arrow’s Theorem

  • Universality. The voting method should provide a complete

ranking of all alternatives from any set of individual preference ballots. Pareto optimality.

Todd Hester

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SLIDE 67

Arrow’s Theorem

  • Universality. The voting method should provide a complete

ranking of all alternatives from any set of individual preference ballots. Pareto optimality. If everyone prefers X to Y, then the

  • utcome should rank X above Y

.

Todd Hester

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SLIDE 68

Arrow’s Theorem

  • Universality. The voting method should provide a complete

ranking of all alternatives from any set of individual preference ballots. Pareto optimality. If everyone prefers X to Y, then the

  • utcome should rank X above Y

. Criterion of independence of irrelevant alternatives.

Todd Hester

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SLIDE 69

Arrow’s Theorem

  • Universality. The voting method should provide a complete

ranking of all alternatives from any set of individual preference ballots. Pareto optimality. If everyone prefers X to Y, then the

  • utcome should rank X above Y

. Criterion of independence of irrelevant alternatives. If

  • ne

set of preference ballots would lead to an an overall ranking of alternative X above alternative Y and if some preference ballots are changed without changing the relative rank of X and Y, then the method should still rank X above Y .

Todd Hester

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SLIDE 70

Citizen Sovereignty.

Todd Hester

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SLIDE 71

Citizen Sovereignty. Every possible ranking of alternatives can be achieved from some set of individual preference ballots.

Todd Hester

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SLIDE 72

Citizen Sovereignty. Every possible ranking of alternatives can be achieved from some set of individual preference ballots. Non-dictatorship.

Todd Hester

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Citizen Sovereignty. Every possible ranking of alternatives can be achieved from some set of individual preference ballots. Non-dictatorship. There should not be one specific voter whose preference ballot is always adopted.

Todd Hester

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SLIDE 74

Arrow’s Theorem

Universality.

Todd Hester

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SLIDE 75

Arrow’s Theorem

  • Universality. Complete rankings

Todd Hester

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SLIDE 76

Arrow’s Theorem

  • Universality. Complete rankings

Pareto optimality.

Todd Hester

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SLIDE 77

Arrow’s Theorem

  • Universality. Complete rankings

Pareto optimality. X > Y if all agree

Todd Hester

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SLIDE 78

Arrow’s Theorem

  • Universality. Complete rankings

Pareto optimality. X > Y if all agree Citizen Sovereignty.

Todd Hester

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SLIDE 79

Arrow’s Theorem

  • Universality. Complete rankings

Pareto optimality. X > Y if all agree Citizen Sovereignty. Any ranking possible

Todd Hester

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SLIDE 80

Arrow’s Theorem

  • Universality. Complete rankings

Pareto optimality. X > Y if all agree Citizen Sovereignty. Any ranking possible Non-dictatorship.

Todd Hester

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SLIDE 81

Arrow’s Theorem

  • Universality. Complete rankings

Pareto optimality. X > Y if all agree Citizen Sovereignty. Any ranking possible Non-dictatorship. No one voter decides

Todd Hester

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SLIDE 82

Arrow’s Theorem

  • Universality. Complete rankings

Pareto optimality. X > Y if all agree Citizen Sovereignty. Any ranking possible Non-dictatorship. No one voter decides Independence of irrelevant alternatives.

Todd Hester

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SLIDE 83

Arrow’s Theorem

  • Universality. Complete rankings

Pareto optimality. X > Y if all agree Citizen Sovereignty. Any ranking possible Non-dictatorship. No one voter decides Independence of irrelevant alternatives. Removing or adding a non-winner doesn’t change winner

Todd Hester

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SLIDE 84

Arrow’s Theorem

  • Universality. Complete rankings

Pareto optimality. X > Y if all agree Citizen Sovereignty. Any ranking possible Non-dictatorship. No one voter decides Independence of irrelevant alternatives. Removing or adding a non-winner doesn’t change winner Not all possible!

Todd Hester

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SLIDE 85

Condorcet Voting

  • Strategy

proof under weaker irrelevant alternatives criterion

Todd Hester

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SLIDE 86

Condorcet Voting

  • Strategy

proof under weaker irrelevant alternatives criterion

  • A pairwise method

Todd Hester

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SLIDE 87

Condorcet Voting

  • Strategy

proof under weaker irrelevant alternatives criterion

  • A pairwise method
  • Smith set:

smallest set of candidates such that each candidate in the set preferred over each candidate not in the set

Todd Hester

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SLIDE 88

Condorcet Voting

  • Strategy

proof under weaker irrelevant alternatives criterion

  • A pairwise method
  • Smith set:

smallest set of candidates such that each candidate in the set preferred over each candidate not in the set

  • Every candidate in the Smith set is relevant

Todd Hester

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SLIDE 89

Condorcet Example

  • 48: A > B > C
  • 40: B > C > A
  • 12: C > B > A

Todd Hester

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SLIDE 90

Condorcet Example

  • 48: A > B > C
  • 40: B > C > A
  • 12: C > B > A
  • A vs. B :

Todd Hester

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SLIDE 91

Condorcet Example

  • 48: A > B > C
  • 40: B > C > A
  • 12: C > B > A
  • A vs. B : 48 – 52 =

⇒ B > A

Todd Hester

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SLIDE 92

Condorcet Example

  • 48: A > B > C
  • 40: B > C > A
  • 12: C > B > A
  • A vs. B : 48 – 52 =

⇒ B > A

  • A vs. C : 48 – 52 =

⇒ C > A

  • B vs. C : 88 – 12 =

⇒ B > C

Todd Hester

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SLIDE 93

Condorcet Example

  • 48: A > B > C
  • 40: B > C > A
  • 12: C > B > A
  • A vs. B : 48 – 52 =

⇒ B > A

  • A vs. C : 48 – 52 =

⇒ C > A

  • B vs. C : 88 – 12 =

⇒ B > C Overall: B > C > A

Todd Hester

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SLIDE 94

Condorcet Example

  • 48: A > B > C
  • 40: B > C > A
  • 12: C > B > A
  • A vs. B : 48 – 52 =

⇒ B > A

  • A vs. C : 48 – 52 =

⇒ C > A

  • B vs. C : 88 – 12 =

⇒ B > C Overall: B > C > A

  • Does that solve everything?

Todd Hester

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SLIDE 95

Condorcet Example

  • 48: A > B > C
  • 40: B > C > A
  • 12: C > B > A
  • A vs. B : 48 – 52 =

⇒ B > A

  • A vs. C : 48 – 52 =

⇒ C > A

  • B vs. C : 88 – 12 =

⇒ B > C Overall: B > C > A

  • Does that solve everything? What about cycles?

Todd Hester