Promotion of Cooperation in Public Goods Game by Socialized - PowerPoint Presentation

Slide1

Promotion of Cooperation in Public Goods Game by Socialized Speed-Restricted Movement

Pengyuan Du, Mario

Gerla

Department

of Computer Science,

UCLA,

USASlide2

What is the paper all about?Consider commerce in medieval FranceA citizen lives in a community, he moves around to offer his products/services to others and expects products/services in turn

Public Good increases with commerce; but there is the risk of no returns

So, Cooperators (entrepreneurs) take risks; Defectors (

ie, conservatives) do not trade We want to understand how the movement of citizens beyond their homes can help the Public Good

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OutlineIntroductionSystem ModelSSRM Approximated Degree Distribution

Simulation Study of Cooperation

Conclusion

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IntroductionThe evolution of social interactions: from medieval France to Mobile CommunicationsRapid growth of mobile devices and users re-proposes the social collaboration at different levels and different Public GoodsWireless CooperationMobile users can benefit from collaboration

Collaboration may help overcome critical challenges in mobile environment, e.g. energy, connectivity, spectrum scarcity, global info scarcity, etc.

Example Applications

Packet Forwarding in DTNCooperative video streamingCrowdsourcing4 of 26Slide5

IntroductionCooperation is not freeRisk of non reciprocation by diffidents/selfishSelfishness leads to the tragedy of commonsCredit or reputation based systems stimulate cooperation

We study it with

Evol

. Game Theory (EGT)A branch of Game Theory that investigates cooperative behaviorsNo centralized management and information exchangeMobile users are involved in pairwise/group interactions, and make decisions rationallyFocusing on the evolutionarily stable strategy5 of 26Slide6

Introduction

EGT Setup

Two strategies: Cooperator (C), or Defector (D)

There is payoff from playing the social dilemma game

Reproduction model favors the “reproduction”

ie

mimicking of strategies of successful individuals (with higher payoff)

Similar to Darwinian species evolution: the fittest prevail

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Social

Dilemma Games

Reproduction

model

Next

round

strategies

Current

strategies

1

st

Round

10000

th

RoundSlide7

Related WorkStatic Network[1]Network structure; Payoff heterogeneity; Strategic complexityMobile Network[2][3]

Random

but

homogeneous movement7 of 26

1] Perc

,

Matjaž

, et al. "Evolutionary dynamics of group interactions on

structured

populations: a review." 

Journal of the royal society interface

 10.80 (2013): 20120997.

[2]

Cardillo

,

Alessio

, et al. "Velocity-enhanced cooperation of moving agents playing public goods games." Physical Review E 85.6 (2012): 067101.

[

3] Antonioni

, Alberto, Marco

Tomassini

, and Pierre

Buesser. "Random diffusion and cooperation in continuous two-dimensional space." Journal of theoretical biology 344 (2014): 40-48.Slide8

ContributionsWe propose a Socialized Speed-Restricted Mobility (SSRM) model to represent realistic human movement

We show that two common social network structures, with

Power-law

and Exponential degrees, are generated by SSRMShow via analysis and simulation that SSRM mobility promotes the emergence of cooperation8 of 26Slide9

System ModelSSRM model: node i move within area A1

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Homogeneous:

Uniform

Heterogeneous:

Exponential

-Pareto

 Slide10

System ModelNetwork Large 2D circular spaceMobile users are initially distributed in the space according to Poisson Point Process with density 1 (home location)

SSRM model

Each user has a circular moving area around the home location

drawn from specific probability distributionRandom and independent movement within10 of 26Slide11

System ModelNeighbor Collection ProcessEvery user g

time steps, and communicates with neighbors within range

It “collects” neighbors met at each time

step (=

degree

)

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Neighbor Collection Process

For Slide12

System ModelPublic Goods Game (PGG)Users initially random pick a strategy: C/D Each user plays the PGG with collected neighbors at the end of collection processCooperators contribute after each PGG game Defectors contribute nothing yet get benefit (free loaders)

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Public Good IncreaseIn a single PGG game, the community gathers the contributions of Cooperators and multiplies them by an enhancement factor r.

The contributions are

equally distributed among all the

participants (including Defectors)The entire system is driven by the goal of increasing the PG Steady PG increase is guaranteed by strong fraction of Collaborators 13 of 26Slide14

System ModelStrategy Update at the end of every PG GameEach user i randomly picks one of its neighbors j, and borrows its strategy with probability P[

i

takes j’s strategy]=

Where is the payoff i obtained from all its PGG games. What does the MAX at numerator mean if you have already selected you neighbor??? What are you maximizing over?14 of 26Slide15

Degree DistributionWorking ApproximationApproximate with the number of users whose home locations reside in , denoted by Main result

Homogeneous case

Heterogeneous caseExponential CCDFPareto CCDF

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Approximating SSRM Degree DistributionNumerical Validation

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Approximating SSRM Degree Distribution

Numerical validation

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How does Cooperation evolve?Matlab Simulation setup 10000 epochs of

time

steps

Cooperation is promoted if the fraction of cooperators is close to 1 at relatively small In theory, cooperation prevails at in an infinite, well-mixed population [1]Every data point is the average of 5 repeated simulations

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[1] Santos

, Francisco C., Marta D. Santos, and Jorge M. Pacheco. "Social diversity promotes the emergence of cooperation in public goods games." 

Nature

 454.7201 (2008): 213-216.Slide19

Evolution of Cooperation Simultaneous evolution of Mobility and Strategy, the homogeneous SSRM mobility is consistent with previous random mobility studies

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High cooperation when mobility is moderate

Low cooperation when mobility is increased toSlide20

Evolution of Cooperation Comparing homogeneous and heterogeneous SSRMThe average moving radius for cooperation to prevailHeterogeneity does not help

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Evolution of Cooperation Cooperation is promoted under the same settings Heterogeneous SSRM is better than homogeneous case

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Heterogeneous

Heterogeneous

Homogeneous

HomogeneousSlide22

Explaining the promotion1. Stability metricAverage number of neighbors in M epochs over the number of distinct neighbors in M epochs

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Explaining the promotion2. Degree HeterogeneityExponential and Power-law tails are heavier than PoissonMore high degree users in the heterogeneous modelThe high degree users and their neighbors form clusters similar to social communities

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Cooperative Behaviors of Heterogeneous Mobile UsersTwo instances of heterogeneous mobile network , Exponential withPareto withWe examine

degree, cooperation rate and strategy update frequency

Group mobile users based on the moving area

Data points are the average of 100 epochs after the evolution enters enquilibruim24 of 26Slide25

Degree in different moving area groupsCooperation rate in different moving area groupsStrategy update frequency in moving area groups

Cooperative Behaviors of Heterogeneous Mobile Users

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Cooperative Behaviors of Heterogeneous Mobile UsersSnapshots in exponential mobile networkC-blueD-red6 “hub”s

C-green

D-

yello26 of 26Slide27

ConclusionWe employ the EGT framework to study cooperative behavior in mobile networksA socialized mobility model SSRM to drive the movementPGG and strategy update occur after every neighbor collection processWe verify that SSRM produces Exponential and Power-law degree networks

Cooperation is promoted in mobile social networks due to the

degree heterogeneity

and regular moving patterns27 of 26