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Game and Evolutionary Game in Communication Networks. Yuedong Xu 2013.12.04. Outline. Game Theory: A Premier Evolutionary Game Applications to Networks Potential Research Fields. Using as less math as possible !. 2. 2. Game Theory: A Premier. What is “game” about? Game of Chicken

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outline
Outline
  • Game Theory: A Premier
  • Evolutionary Game
  • Applications to Networks
  • Potential Research Fields

Using as less math

as possible !

game theory a premier

2

2

Game Theory: A Premier
  • What is “game” about?
  • Game of Chicken
    • driver who swerves away looses
  • What should drivers do?
    • To swerve or to stay?
game theory a premier1

2

2

Game Theory: A Premier
  • What is “game” about?
  • Game of Chicken
    • driver who swerves away looses

Driver 2

Drivers want to do opposite of one another

Driver 1

game theory a premier2
Game Theory: A Premier
  • A Game consists of
    • at least two players
    • a set of strategiesfor each player
    • a payofffor each strategy profile
  • Basic assumption (rationality of players)
  • Nash Equilibrium
    • no player can improve its payoff by unilaterallychanging its strategy
  • Pareto optimality, price of anarchy
game theory a premier3
Game Theory: A Premier

Classification 1:

  • Non-Cooperative (Competitive) Games
    • individualized play
  • Cooperative Games
    • play as a group
  • Repeated, Stochastic and Evolutionary Games
    • not one shot
game theory a premier4
Game Theory: A Premier

Classification 2:

game theory a premier5
Game Theory: A Premier

Internet Application

v

C(x) = x

C(x) = 1

C(x) = 0

s

t

C(x) = 1

C(x) = x

w

Selfish Routing game

game theory a premier6
Game Theory: A Premier

Internet Application

P2P Networks: Bittorrent, Xunlei, Pplive, PPStream, QQLive …

game theory a premier7
Game Theory: A Premier

Internet Application

Internet Ecosystem (Business Models)

game theory a premier8
Game Theory: A Premier

Internet Application

Cloud Computing game

game theory a premier9
Game Theory: A Premier

Internet Application

Online Social Networks

game theory a premier10
Game Theory: A Premier

Internet Application

Network Security Game

game theory a premier11
Game Theory: A Premier

Wireless Application

802.11 multiple access game

game theory a premier12
Game Theory: A Premier

Wireless Application

3G/4G Power Control Game

game theory a premier13
Game Theory: A Premier

Wireless Application

?

Green

Blue

?

Packet forwarding game

game theory a premier14
Game Theory: A Premier

Wireless Application

Cognitive radio network game

game theory a premier15
Game Theory: A Premier

Wireless Application

E

Wireless jamming and eavesdrop games

outline1
Outline
  • Game Theory: A Premier
  • Evolutionary Game
  • Applications to Networks
  • Potential Research Fields
recap
Recap
  • Classical game theory (CGT)
    • Outcome depends on strongrationality assumption
    • Each individual uses a strategy that is the "best response" to other players’ choice
    • Question: what is the meaning of a symmetric NE , ,given a large number of players?

Follow the crowd!

evolutionary game theory
Evolutionary game theory
  • Evolutionary game theory (EGT)
    • refinement of CGT
    • game in a population
    • dynamics of strategy adoption
    • mutual learning among players

Evolutionary game theory differs from classical game theory by focusing more on the dynamics of strategy change as influenced not solely by the quality of various competing strategies, but by the effect of frequency with which the various competing strategies are found in the population.

evolutionary game theory1
Evolutionary game theory
  • Evolutionary game theory (EGT)
    • Usually two types of game: games against the field and games with pairwise contests

A game against the field is one in which there is no specific “opponent”

for a given individual - their payoff depends on what everyone in the

population is doing. Ex: Choice of Gender

A pairwise contest game describes a situation in which a given

individual plays against an opponent that has been randomly selected

(by nature) from the population and the payoff depends just on what

both individual do. Ex: Hawk-Dove Game

evolutionary game theory2
Evolutionary game theory
  • A profile of evolutionary game
  • Payoff (fitness)

Given a set of pure strategy S. A population profile is a vector x that gives a probability x(s) with which each strategy s Sis played in the population.

Consider a particular individual in the population with profile x. If that individual uses a profile σ={,}, the individual’s payoff is denoted as . The payoff of this strategy for a pair-wise game is

evolutionary game theory3
Evolutionary game theory
  • Evolutionary stable strategy (ESS)
  • Theorem (ESS)

An evolutionarily stable strategy is a strategy which, if adopted by a population of players, cannot be invaded (or replaced) by any alternative strategy that is initially rare.

evolutionary game theory4
Evolutionary game theory
  • Example (Hawk-Dove Game)
    • H: aggressive; D: mild
    • Population strategy
    • Mixed strategy (H,D) of an individual
    • Payoff matrix (v<c):
    • Suppose the existence of an ESS
evolutionary game theory5
Evolutionary game theory
  • Example (Hawk-Dove Game) ‘cont
    • In the population, the payoff of a mutant is
evolutionary game theory7
Evolutionary game theory
  • ESS
    • no statement of dynamics
    • monomorphic / polymorphic
  • Replicator Dynamics
    • individuals, called replicator, exist in several different types (e.g Hawk and Dove)
    • each type of individual uses a pre-programmed strategy and pass it to its descendants
    • individuals only use PURE strategy in a finite set
    • the population state is ,where is fraction of individuals using strategy
evolutionary game theory8
Evolutionary game theory
  • Replicator Dynamics
    • Fixed point:
    • Stability of fixed point:
    • Stability proof:

Lyapunov stability vs asymptotic stability

Lyapunovfunction and Engenvalue approach

evolutionary game theory9
Evolutionary game theory
  • ESSvs NE in associated two-player game
    • An ESS is a (mixed) NE
    • A NE might not be an ESS
      • Asymmetric NE in monomorphic population
      • Unstable NE
evolutionary game theory10
Evolutionary game theory
  • Replicator dynamics and NE
    • In a two-strategy game
      • Any NE is a fixed point of replicator dynamics
      • Not every fixed point corresponds to a NE
  • Replicator dynamics and ESS
    • ESS is an asymptotically stable fixed point
    • Two strategy pair-wise contest
    • More than two strategies

ESS  Asymp. Stable f.p. sym. NEf.p.

ESS Asymp. Stable f.p. sym. NEf.p.

outline2
Outline
  • Game Theory: A Premier
  • Evolutionary Game
  • Applications to Networks
  • Potential Research Fields

Peer-to-peer file sharing

Wireless networks

peer to peer file sharing
Peer-to-peer file sharing
  • File  Piece (e.g. chunk, block)
    • A content is split in pieces
    • Each piece can be independently downloaded
  • Leecher
    • A peer that is client and server
    • In the context of content delivery
      • Has a partial copy of the content
  • Seed
    • A peer that is only server
    • In the context of content delivery
      • Has a full copy of the content
slide34
Great improvement over customer-server mode

Ideal system: single chunk, fully cooperative

Big System: many peers, many chunks, stochastic system

Peer-to-peer file sharing

Seed

t=0

t=T

t=2T

Which peers shall I serve in each time slot?

time

peer to peer file sharing1
Peer-to-peer file sharing
  • If no good incentive strategy
    • Slow service
    • Even overwhelmed by requests
  • Incentive model
    • A strategyis the behavior (providing/rejecting a service) of a peer against other peers
    • A policy is the set of rules of for incentivization
    • A point is a utility measure of peers
    • A system is robust : convergence and cooperation

Q. Zhao, J. Lui, D. Chiu“AMathematical Framework for Analyzing Adaptive Incentive Protocols in P2P Networks”, IEEE/ACM Trans. Networking, 2012

peer to peer file sharing2
Peer-to-peer file sharing
  • Incentive model (’cont)
    • Strategy = type of peer
    • Finite strategies
      • {cooperator, defector, reciprocator}

Always serve

Always reject

Serve cooperators and reciprocators

with certain probabilities,

reject defectors

peer to peer file sharing3
Peer-to-peer file sharing
  • Incentive model (’cont)
    • System description:
    • Incentive scheme (esp. for reciprocators)

At the beginning of each time slot, each peer randomly selects another peer to request for service. The selected peer chooses to serve the request based on his current strategy. A peer obtains α points if its request is served and loses β (=1) points if it provides service to others.

- Prob. that a type i peer provides service to a type j peer

peer to peer file sharing4
Peer-to-peer file sharing
  • Utility model
    • After a long way, the points gained by a type-i peer
  • We can now study
    • equilibrium state (given G)
    • is the equilibrium stable?
    • how to reach this equilibrium?
    • how good is the incentive scheme

Type-i payoff

Network payoff

Is this enough?

peer to peer file sharing5
Peer-to-peer file sharing
  • Learning model in P2P networks
    • Current best learning model

At the end of each slot, a peer chooses to switch to another strategy s’ with certain prob. To decide which strategy to choose, the peer learns from other peers.

Needs to compute the gains of all other peers !

peer to peer file sharing6
Peer-to-peer file sharing
  • Learning model in P2P networks
    • Opportunistic learning model

At the end of each slot, each peer chooses another peer as its teacher with certain prob. If the teacher is of a different type and performs better, this peer adapts to the teacher’s strategy with another prob.

Simpler !

peer to peer file sharing7
Peer-to-peer file sharing
  • Now we can study
    • Robustness of incentive scheme
      • Mirror incentive policy
        • reciprocators are tit-for-tat
      • Proportional incentive policy
        • A reciprocators always serves any other reciprocator
      • Linear incentive policy

Prob. That reciprocators serve other types of peers!

Each scheme generates a different matrix G !

peer to peer file sharing9
Peer-to-peer file sharing
  • In relation to EG
    • pair-wise contest population game
    • peers players; chunk exchange2 players games

Opp. Learning

Curr. Best Learning

After some efforts

Replicator dynamics

large scale wireless networks
Large-scale wireless networks
  • Random multiple access (slotted ALOHA)
    • A node transmits with prob. p in each slot
    • Simultaneous transmission  collisions
large scale wireless networks1
Large-scale wireless networks
  • Power control game

(signal to noise interference ratio, SINR)

    • Large power  better throughput
    • Large power  more interference to other receivers
large scale wireless networks3
Large-scale wireless networks
  • Sad facts:
    • Selfishness is unsuccessful
    • Optimal cooperation is hard in a large distributed networks (bargaining, Shapley value)
  • Evolutionary game kicks in!

What if wireless nodes learn from each other

in local interactions?

H. Tembine, E. Altman, “Evolutionary Games in Wireless Networks”, IEEE Trans. Syst. Man Cyber. B, 2010

large scale wireless networks4
Large-scale wireless networks
  • Challenges
    • Standard EGT: a player interacts with all other players (or average population)
    • Large-scale wireless networks:
      • no longer strategic pair-wise competition
      • random number of local players
      • non-reciprocal interactions
    • Finite strategies of a player

{transmit, stay quiet} in multiple access game

{high power, low power} in power control game

Non standard EGT

 Standard EGT

large scale wireless networks5
Large-scale wireless networks
  • WCDMA power control game
    • SINR with distance r between transmitter and receiver of node i is given by

PL

PH

PH

Pi: the strategy of node i (i.e., PH or PL)

x : the proportion of the population choosing PH

g : channel gain, r0 is the radius-of-reception circle of receiver

α : the attenuation order with value between 3 and 6, σ : the noise power, and β: the inverse of processing gain

I(x): total interference from all nodes to the receiver of node i

large scale wireless networks6
Large-scale wireless networks
  • WCDMA power control game
    • Payoff of node i is as follows:

R: transmission range

wp : cost weight due to adopting power

Pi (e.g. energy consumption)

ζ(r) : probability density function given the density of receiver

large scale wireless networks7
Large-scale wireless networks
  • WCDMA power control game
    • Existence of uniqueness of ESS
      • Replicator dynamics

This function is continuous and strictly monotonic, which is required for the proof of stability based on sufficient condition

large scale wireless networks8
Large-scale wireless networks
  • Some other related works
    • Extensions to EGT
    • Applications

E. Altman, Y. Hayel. “Markov Decision Evolutionary Games”, IEEE Trans. Auto. Ctrl. 2010

X. Luo and H. Tembine. “Evolutionary Coalitional Games for Random Access Control”, IEEE Infocom 2013 (mini)

P. Coucheney, C. Touati. “Fair and Efficient User-Network Association Algorithm for Multi-Technology Wireless Networks”, IEEE Infocom 2009 (mini)

S. Shakkottai, E. Altman. “The Case for Non-cooperative Multihomingof Users to Access Points in IEEE 802.11 WLANs”, IEEE Infocom 2006

C. Jiang, K. Liu, “Distributed Adaptive Networks: A Graphical Evolutionary Game-Theoretic View”, IEEE Trans. Signal Processing, 2013

large scale wireless networks9
Large-scale wireless networks
  • Summary
    • P2P : practical problem  EG theory
    • WCDMA: EG theory  practical problem
    • Common Challenges:
      • difficultto find important problem
      • difficultto have theoretical contributions to EGT

Two different styles !