file1

Introduction to Game Theory and its Applications in Computer Networks John C.S. Lui Dept. of Computer Science & Engineering The Chinese University of Hong Kong Daniel R. Figueiredo School of Computer and Communication Sciences Swiss Federal Institute of Technology – Lausanne (EPFL) ACM SIGMETRICS / IFIP Performance June 2006

Tutorial Organization ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

What is Game Theory About? ,[object Object],[object Object],[object Object],[object Object],[object Object],2 2

Applications of Game Theory ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Limitations of Game Theory ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

What is a Game? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Classification of Games ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Matrix Game (Normal form) ,[object Object],[object Object],[object Object],Player 1 Player 2 Strategy set for Player 1 Strategy set for Player 2 Payoff to Player 1 Payoff to Player 2 ,[object Object],(3, 4) (0, 0) B (3, -1) (-5, 1) B (-2, -1) (2, 2) A C A

More Formal Game Definition ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Two-person Zero-sum Games ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Analyzing the Game ,[object Object],Player 1 Player 2 Strictly dominated strategy (dominated by C) Strictly dominated strategy (dominated by B) -1 2 1 -16 D 3 4 2 5 C -18 3 1 3 B 0 1 -1 12 A D C B A

Dominance ,[object Object],[object Object],[object Object],[object Object],[object Object]

Solving the Game Player 1 Player 2 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],3 2 3 B 4 -1 -2 T R M L

Solving the Game Player 1 Player 2 ,[object Object],[object Object],[object Object],[object Object],-1 0 -16 D 3 2 5 C 0 -1 12 A D B A

Analyzing the Game Player 1 Player 2 ,[object Object],[object Object],-1 0 -16 D 3 2 5 C 0 -1 12 A D B A

Saddle Points ,[object Object],[object Object],[object Object],[object Object],[object Object]

Why Play Saddle Points? ,[object Object],[object Object],[object Object],[object Object],Player 1 Player 2 -1 0 -16 D 3 2 5 C 0 -1 12 A D B A

Why Play Saddle Points? ,[object Object],[object Object],[object Object],[object Object],Player 1 Player 2 -1 0 -16 D 3 2 5 C 0 -1 12 A D B A Powerful arguments to play saddle point!

Solving the Game (min-max algorithm) ,[object Object],[object Object],[object Object],Player 1 Player 2 ,[object Object],[object Object],[object Object],[object Object],-5 -4 8 0 D 3 1 5 7 C -1 0 2 -10 B 5 2 3 4 A D C B A -5 1 -10 2 5 2 8 7

Multiple Saddle Points Player 1 Player 2 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],-5 -4 0 8 D 3 2 2 5 C -1 0 -10 2 B 5 2 2 3 A D C B A -5 2 -10 2 5 2 2 8

Games With no Saddle Points ,[object Object],[object Object],Player 1 Player 2 3 0 B 1 -5 B -1 2 A C A

Mixed Strategies ,[object Object],[object Object],[object Object],Player 1 Payoff to P1 when playing A = 1/3(4) + 2/3(0) = 4/3 Payoff to P1 when playing B = 1/3(-5) + 2/3(3) = 1/3 ,[object Object],3 0 D -5 B 4 A C 2/3 1/3

Mixed Strategies ,[object Object],[object Object],[object Object],Player 1 Payoff to P1 when playing A = x(4) + (1-x)(0) = 4x Payoff to P1 when playing B = x(-5) + (1-x)(3) = 3 – 8x 4x = 3 – 8x, thus x = 1/4 ,[object Object],3 0 D -5 B 4 A C (1-x) x

Mixed Strategies ,[object Object],[object Object],[object Object],[object Object],Player 1 Payoff to P2 when playing C = x(-4) + (1-x)(5) = 5 - 9x Payoff to P2 when playing D = x(0) + (1-x)(-3) = -3 + 3x 5 – 9x = -3 + 3x, thus x = 2/3 Player 2 Payoff to P2 = -1 3 0 D -5 B 4 A C (1-x) x

Minimax Theorem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Two-person Non-zero Sum Games ,[object Object],[object Object],Player 1 Player 2 ,[object Object],[object Object],-1, 2 2, 0 B 5, 1 B 3, 4 A A

What is the Solution? ,[object Object],[object Object],[object Object],[object Object],Player 1 Player 2 Player 1 Player 2 2, 1 -1, 4 B 3, 2 B 5, 0 A A -1, 2 2, 0 B 3, 1 B 5, 4 A A

Multiple Solution Problem ,[object Object],[object Object],[object Object],Player 1 Player 2 equilibria 2, 2 1, 1 B 0, 1 B 1, 4 A A

The Good News: Nash’s Theorem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

The Prisoner’s Dilemma ,[object Object],[object Object],[object Object],[object Object],Suspect 1 Suspect 2 payoff is years in jail ( smaller is better ) single NEP better outcome 5, 5 10, 1 C 1, 10 C 2, 2 S S

Pareto Optimal ,[object Object],Suspect 1 Suspect 2 ,[object Object],[object Object],[object Object],Pareto Optimal 5, 5 10, 1 C 1, 10 C 2, 2 S S

Game of Chicken Revisited ,[object Object],[object Object],Driver 1 Driver 2 Drivers want to do opposite of one another Will prior communication help? 2 2 -10, -10 -1, 5 stay 5, -1 stay 0, 0 swerve swerve

Example: Cournot Model of Duopoly ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],How much should firm i produce?

Example: Cournot Model of Duopoly ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example: Cournot Model of Duopoly ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],value chosen by firm 2 value chosen by firm 1

Example: Cournot Model of Duopoly ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],and and

Example: Cournot Model of Duopoly ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],less quantity produced higher price Competition can be good!

Example: Cournot Model of Duopoly ,[object Object],[object Object],[object Object],NEP : strategies are mutual best responses ,[object Object]

Game Trees (Extensive form) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Game Trees Example ,[object Object],Player 1 Player 2 Player 2 L L R R R L 3, 1 1, 2 -2, 1 0, -1 ,[object Object],what to do when P1 plays L what to do when P1 plays R ,[object Object],Payoff to Player 2 Payoff to Player 1

More Formal Extensive Game Definition ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Game Tree Example ,[object Object],[object Object],[object Object],[object Object],Microsoft Mozilla Mozilla .net .net java java java .net 3, 1 1, 0 0, 0 2, 2

Converting to Matrix Game ,[object Object],[object Object],Microsoft Mozilla 0, 0 1, 0 java, .net 2, 2 3, 1 .net, java 2, 2 0, 0 java 1, 0 3, 1 .net java, java .net, .net .net .net java java java .net 3, 1 1, 0 0, 0 2, 2

NEP and Incredible Threats Microsoft Mozilla NEP incredible threat ,[object Object],[object Object],.net .net java java java .net 3, 1 1, 0 0, 0 2, 2 0, 0 1, 0 java, .net 2, 2 3, 1 .net, java 2, 2 0, 0 java 1, 0 3, 1 .net java, java .net, .net

Solving the Game (backward induction) ,[object Object],[object Object],Best strategy for Mozilla: .net, java (follow Microsoft) Best strategy for Microsoft: .net ,[object Object],[object Object],Equilibrium outcome .net java 3, 1 2, 2 .net .net java java java .net 3, 1 1, 0 0, 0 2, 2

Backward Induction on Game Trees ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Leaders and Followers ,[object Object],[object Object],Mozilla: java Microsoft: .net, java ,[object Object],[object Object],[object Object],[object Object],Mozilla Microsoft Microsoft .net .net java java java .net 1, 3 0, 1 0, 0 2, 2

The Subgame Concept ,[object Object],[object Object],[object Object],[object Object],Microsoft Mozilla Mozilla .net .net java java java .net 3, 1 1, 0 0, 0 2, 2

Subgame Perfect Nash Equilibrium ,[object Object],[object Object],[object Object],[object Object],[object Object]

Subgame Perfect Nash Equilibrium ,[object Object],[object Object],[object Object],MS Mozilla J N Subgame Perfect NEP Not subgame Perfect NEP Microsoft Mozilla Mozilla .net .net java java java .net 3, 1 1, 0 0, 0 2, 2 0,0 1,0 JN 2,2 3,1 NJ 2,2 0,0 J 1,0 3,1 N JJ NN

file1

Empfohlen

Empfohlen

Weitere ähnliche Inhalte

Was ist angesagt?

Was ist angesagt? (20)

Ähnlich wie file1

Ähnlich wie file1 (20)

Mehr von webuploader

Mehr von webuploader (20)

Kürzlich hochgeladen

Kürzlich hochgeladen (20)

file1