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Nash Equilibrium - Thinking Like Computers - Lecture Slides, Slides of Artificial Intelligence

Bidhan Chandra Krishi ViswavidyalayaArtificial Intelligence

During the course work of Thinking Like Computers, we study the key concept of artificial intelligence. The main points in these lecture slides are:Nash Equilibrium, Payoff Matrix, Symmetric Interaction, Game of Chicken, Multi-Agent Interactions, Design Protocols, Mechanism Design, Pirates’ Democracy, Auctioneer and Bidders, Vickrey Auctions, Lies and Collusion

Typology: Slides

2012/2013

Uploaded on 04/24/2013

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CSCI 100
Think Like Computers
Lecture 26
Fall 2008
Last Time …
•Nash Equilibrium
•Prisoner’s Dilemma
•Other 2x2 symmetric game
Stag hunt
Identify a Nash Equilibrium
in the Payoff Matrix
Y9
X9
Y8
X8
Y7
X7
C
Y5
X5
Y2
X2
V
Y6
X6
Y4
X4
B
Y3
X3
Y1
X1
A
WU
Each Nash Equilibrium: max X for its column AND max Y for its row
2x2 Symmetric Interaction
W
W
Y
Z
C
Z
Y
X
X
D
CD
Prisoner’s dilemma: Y > W > X > Z
One Nash equilibrium: (D, D)
3
3
5
0
C
0
5
2
2
D
CD
The Game of Chicken
•To establish who is bravest out of two
young thugs.
•Both drive their cars at high speed towards
a cliff.
•The least brave of the two (the ‘chicken’)
will be the first to drop out of the game by
steering away from the cliff.
Chicken
2
2
3
1
C (steer away)
1
3
0
0
D
C (steer away)D
Nash equilibrium?
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pf4

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Download Nash Equilibrium - Thinking Like Computers - Lecture Slides and more Slides Artificial Intelligence in PDF only on Docsity!

CSCI 100

Think Like Computers

Lecture 26

Fall 2008

Last Time …

  • Nash Equilibrium
  • Prisoner’s Dilemma
  • Other 2x2 symmetric game Š Stag hunt

Identify a Nash Equilibrium

in the Payoff Matrix

Y

X

Y

X

Y

X

C

Y

X

Y

X

V

Y

X

Y

X

B

Y

X

Y

X

A

U W

Each Nash Equilibrium: max X for its column AND max Y for its row

2x2 Symmetric Interaction

W

W

Y

Z

C

Z

Y

X

X

D

D C

Prisoner’s dilemma: Y > W > X > Z One Nash equilibrium: (D, D) 3 3

5 0

C

0 5

2 2

D

D C

The Game of Chicken

  • To establish who is bravest out of two

young thugs.

  • Both drive their cars at high speed towards

a cliff.

  • The least brave of the two (the ‘chicken’)

will be the first to drop out of the game by

steering away from the cliff.

Chicken

2 2

3 1

C (steer away)

1 3

0 0

D

D C (steer away)

Nash equilibrium?

Multi-Agent Interactions

  • The key questions: how do we cooperate?
  • An obvious problem: reaching agreements in a society of self-interested agents.
  • Some interactions are zero-sum. Š What does this mean?
  • However, most other scenarios are not so extreme: Š To reach mutually beneficial agreement on matters of common interest. (Win-win!)

Multi-agent Interactions

  • Negotiation
  • Argumentation
  • They do not occur in a vacuum – they will

be governed by a particular mechanism, or

protocol.

Š “rules of encounter” Š Social norms

Two issues

    1. Design protocols so that the interactions

would have desired outcomes

Š This is known as “mechanism design”

    1. Given a particular protocol, how can a

particular strategy be developed for an

agent so that it can maximize its own

welfare

JFK Quote

  • Ask not what your country can do for you – ask what you can do for your country Š Some retorts: ask not what we can do for our country, because we have done enough. Let's ask our country what they can do for us.
  • Philosophically: Š Self-interested vs Self-less
  • Both are not quite proper things to ask … Š How to make the system better so that every one can do his/her best

Why Mechanism Design?

  • Desired properties of good mechanisms: Š Guaranteed success Š Maximizing social welfare Š Pareto efficiency – can’t happier without hurting anyone else Š Individual rationality (to play by rules) Š Stability (Nash equilibrium for example) Š Simplicity Š Distribution (no single point of failure)

Some Interesting Problems

  • How to divide a cake? Š 2 people? Š N people?

Lies and Collusion

  • These protocols are not immune to lying

and collusion by both bidders and

auctioneers.

  • Examples: Š Grand coalition of bidders Š Auctioneer lying in Vickery auctions Š Shills