1. Pengyuan Du, Mario Gerla Department of Computer Science, UCLA, USA
Promotion of Cooperation in Public Goods Game by Socialized Speed-Restricted Movement
Pengyuan Du, Mario Gerla
Department of Computer Science, UCLA, USA

2. What is the paper all about?
Consider commerce in medieval France
A 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

3. Outline Introduction System Model
SSRM Approximated Degree Distribution
Simulation Study of Cooperation
Conclusion

4. Introduction
The evolution of social interactions: from medieval France to Mobile Communications
Rapid growth of mobile devices and users re-proposes the social collaboration at different levels and different Public Goods
Wireless Cooperation
Mobile 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 DTN
Cooperative video streaming
Crowdsourcing

5. Introduction Cooperation is not free
Risk of non reciprocation by diffidents/selfish
Selfishness leads to the tragedy of commons
Credit or reputation based systems stimulate cooperation
We study it with Evol. Game Theory (EGT)
A branch of Game Theory that investigates cooperative behaviors
No centralized management and information exchange
Mobile users are involved in pairwise/group interactions, and make decisions rationally
Focusing on the evolutionarily stable strategy

6. 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
Social
Dilemma Games
Reproduction
model
Next
round
strategies
Current
strategies
10000th Round
1st Round

7. Related Work Static Network[1] Mobile Network[2][3]
Network structure; Payoff heterogeneity; Strategic complexity
Mobile Network[2][3]
Random but homogeneous movement
1] Perc, Matjaž, et al. "Evolutionary dynamics of group interactions on structured populations: a review." Journal of the royal society interface 10.80 (2013):
[2] Cardillo, Alessio, et al. "Velocity-enhanced cooperation of moving agents playing public goods games." Physical Review E 85.6 (2012):
[3] Antonioni, Alberto, Marco Tomassini, and Pierre Buesser. "Random diffusion and cooperation in continuous two-dimensional space." Journal of theoretical biology 344 (2014):

8. Contributions
We 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 SSRM
Show via analysis and simulation that SSRM mobility promotes the emergence of cooperation

9. System Model SSRM model: node i move within area A1 Homogeneous:
𝐴 𝑖 = 𝐴 𝑢𝑛𝑖 <𝐴 Uniform
Heterogeneous:
𝑓 𝐴 𝑖 𝑎 =𝜆 𝑒 −𝜆𝑎 Exponential
𝑓 𝐴 𝑖 𝑎 = 𝛼 𝜇 𝛼 (𝜇+𝑎) 𝛼 Pareto

10. System Model Network SSRM model Large 2D circular space
Mobile 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 distribution
Random and independent movement within

11. System Model Neighbor Collection Process
Every user goes through 𝜏 time steps, and communicates with neighbors within range 𝐶 𝑟
It “collects” neighbors met at each time step (= degree)
Neighbor Collection Process
For

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

13. Public Good Increase
In 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

14. System Model Strategy Update at the end of every PG Game
Each 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?

15. Degree Distribution Working Approximation Main result
Approximate with the number of users whose home locations reside in , denoted by
Main result
Homogeneous case
Heterogeneous case
Exponential
CCDF
Pareto

16. Approximating SSRM Degree Distribution
Numerical Validation

17. Approximating SSRM Degree Distribution
Numerical validation

18. How does Cooperation evolve?
Matlab Simulation setup
10000 epochs of 𝜏 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
[1] Santos, Francisco C., Marta D. Santos, and Jorge M. Pacheco. "Social diversity promotes the emergence of cooperation in public goods games." Nature  (2008):

19. Evolution of Cooperation
Simultaneous evolution of Mobility and Strategy, the homogeneous SSRM mobility is consistent with previous random mobility studies
High cooperation when mobility is moderate
Low cooperation when mobility is increased to

20. Evolution of Cooperation
Comparing homogeneous and heterogeneous SSRM
The average moving radius
for cooperation to prevail
Heterogeneity does not help

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

22. Explaining the promotion
1. Stability metric
Average number of neighbors in M epochs over the number of distinct neighbors in M epochs

23. Explaining the promotion
2. Degree Heterogeneity
Exponential and Power-law tails are heavier than Poisson
More high degree users in the heterogeneous model
The high degree users and their neighbors form clusters similar to social communities

24. Cooperative Behaviors of Heterogeneous Mobile Users
Two instances of heterogeneous mobile network ,
Exponential with
Pareto with
We 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 enquilibruim

25. Cooperative Behaviors of Heterogeneous Mobile Users
Degree in different moving area groups
Cooperation rate in different moving area groups
Strategy update frequency in moving area groups

26. Cooperative Behaviors of Heterogeneous Mobile Users
Snapshots in exponential mobile network
C-blue
D-red
6 “hub”s
C-green
D-yello

27. Conclusion
We employ the EGT framework to study cooperative behavior in mobile networks
A socialized mobility model SSRM to drive the movement
PGG and strategy update occur after every neighbor collection process
We 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 patterns