4 groups'

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• 4 groups.
• Several rounds of play.
• Each group chooses action A or B in each round.
• Dont let other groups know your choice.
• Submit your choice to me. Then Ill reveal them.
• If all groups choose A, each one gets 150.
• If 3 groups choose A, each of them loses 100.
  The one who chooses B gets 300.
• If 2 groups choose A, each of them loses 200.
  Each one who chooses B gets 200.
• If 1 group chooses A, that group loses 300.
  Each one who chooses B gets 100.
• If all groups choose B, each one loses 150.

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Game Theoretic Approach in Computer
ScienceCS3150, Fall 2002Course Introduction

• Patchrawat Uthaisombut
• University of Pittsburgh

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Basic Information

• Class Meetings
• Tue,Thu 230pm-350pm 6516 Sennott Square
• Instructor Patchrawat Uthaisombut
• Office 5325 Sennott Square
• Office Hours
• Monday 100pm - 300pm
• Thursday 1100am - 1200noon and 100pm - 200pm.
  
• and by appointments
• Email utp_at_cs.pitt.edu
• Web http//www.cs.pitt.edu/utp
• Phone [phone]

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Course Organization

• Lectures
• Game theory and Mechanism Design
• Algorithms Design and Analysis
• Reading papers
• 25-30 papers
• Presentations (55)
• slides, summary, gt3 papers
• Discussions (35)
• submit 3 questions
• class discussions
• Exercises (10)

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Tentative Topics

• Introduction to game theory
• Nash equilibrium and other equilibria
• Introduction to Mechanism design
• Multicast pricing
• Routing and congestion control
• Worst-case equilibria and "the price of anarchy"
• Combinatorial auctions
• Games played by automata and bounded rationality
• Evolutionary game theory and repeated games
• Fairness in cooperative games

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Theoretical Computer Science

• Goal in the past 50 years (1950-2000)
• Study the capabilities and limitations of the von
  Neumann computer --
• which is the most advanced computational model in
  that time period.

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CS Theory in the past 50 years

• Computability theory
• The Halting problem
• Complexity theory
• NP-completeness
• Approximation algorithms
• Limited computational power
• Online algorithms
• Limited knowledge of the future
• Distributed algorithms
• Limited knowledge of global information
• What should be the goal today?

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The Internet
10
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The Internet

• Huge, growing, anarchic
• Built, operated, used by entities with diverse
  interests
• Competing and cooperating
• Lack theoretical understanding at present

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Some Open Problems

• Sharing cost of multicast transmissions
• Congestion control
• Augmenting new resources
• Price of anarchy
• Auctions of digital goods
• What kind of tools can be used?
• Algorithms and Game Theory

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Game Theory

• A subject in Economics
• The study of behaviors and interactions of
  rational agents in competitive and cooperative
  situations.

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The Prisoners Dilemma

• The confession of a suspect will be used against
  the other.
• If both confess, get a reduced sentence.
• If neither confesses, face only minimum charge.

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Mechanism Design

• Game theory
• Given a game and selfish players, what will
  happen?
• Mechanism Design
• Given a goal, design a game so that the players,
  driven by their self-interests, end up achieving
  the goal of the game designer.
• Inverse of game theory

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322
200
643
150
307
750
400
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Multicast Pricing
source
52
30
costs

21
21
40
70
14, 8
9, 5, 5, 3
32
23, 17, 14, 9
17, 10
utilities of agents in the node
(u the intrinsic value of the information to
agent i, known only to agent i)
i
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Computer Science Aspect

• Running time
• Memory usage
• Distributed implementation
• Communication complexity
• Approximation

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Extensive games

• Extensive games
• Games with multiple rounds.
• Possible actions
• Depends on the whole history
• Payoffs
• For each outcome at end of game
• Depends on the whole history
• Decision tree
• Tic-Tac-Toe, Chess

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Repeated Games

• Repeated Games
• A strategic game which is played repeatedly.
• Player payoff
• Sum of the payoff got in each of the rounds.
• Can be represented as extensive games
• Both players make each move simultaneously.

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Repeated Prisoners Dilemma
C,C
D,D
C,D
D,C
-5,-5
0,-10
-10,0
-1,-1




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Rationality

• Ability to reason about the game
• aware of alternatives, has clear preferences
• know that other players are rational.
• Bounded Rationality
• players have limited ability to reason
• poly-time algorithms, limited memory, Etc.
• Concepts of
• Selfishness, Threats, Bluffs, Punishments, Trust,
  Reputation, Lies, Selflessness, Unity, etc.

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Summary

• Played a game
• Course organization
• Motivations
• Game theory
• Mechanism design
• Computer science
• Extensive and repeated games
• Bounded rationality
• FA that play games.