Game Theory with Engineering Application, Study notes of Game Theory

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MS&E

Game

Theory

with

Engineering

Applications

Lecture 1

Ramesh Johari

Outline • Administrative stuff• Course introduction• A game

Administrative

details

• 6-7 problem sets

Assigned Thursday, due followingThursday in box outside Terman 319 No late assignments accepted

• Midterm to be held February 8 (in class)

Big

picture

Economics and engineering are

tied together more than ever Game theory provides a set of tools we can

use to study problems at this interface

Motivating

examples

• Internet resource allocation
  • TCP: regulates flow of packets through the

Internet

• Malicious users can grab much more than

“fair” share

• How do we design “fair”, “efficient”

allocation protocols that are robust togaming?

Motivating

examples

• Electricity markets
  • Electricity can’t be stored, and

must be reliable

• Market failure is disastrous

(e.g., California in 2000)

• How do we design efficient, sustainable

markets?

ISP

contracts

• Transit vs. peer contracts
  • Transit:

If A pays B, thenA agrees to carry all traffic to/from B

• Peer:

A and B are of similar size,and agree to exchange trafficterminating in each other’s network

Problems

in

the

ISP

industry

• In 2002, seven dominant players:
  • Sprint• AT&T• MCI/UUnet• Qwest• C&W• Level3• Genuity

Econ

pt.

war

of

attrition

• Pricing below marginal cost

War of attrition (repeated game):Lose money now in hopes of being last firm standing

Econ

pt.

Bertrand

• Example: • If

p

1

p

, then ISP 2’s profit = zero 2

CNN

ISP 1

ISP 2

peer

“eyeballs”

p^1

p^2

Engineering What is the problem in Bertrand example?ISP 2 receives no credit for the value

generated. Current protocols don’t expedite

transmission of value information. ⇒

How do we build economically robust,informative protocols?

This

course

We will develop the basics of

noncooperative game theory… …but with an eye towards connection with

engineering applications.

Reasoning

about

the

game

• What is the “best” a player can do?• What is the best they can do together?• Should they ever bid zero?• Is there any bid a player should

never

make?

• What is the minimum a player can

guarantee himself or herself?

What will happen when the game isplayed?

Reasoning

about

the

game

Player 1’s payoff = 8 x

w

w

1

w

w

1^ $

$

$

$

$

$4.

$4.

$5.

$6.

$8.

$

$4.

$5.

$5.

$7.

$9.

$

$4.

$5.

$6.

$7.

$10.

$

$4.

$5.

$5.

$7.

$11.

$

$4.

$4.

$4.

$4.

$4.

$

Player 2’s bid

Player 1’s bid