Incentivizing Sharing in Realtime D2D Streaming Networks: A Mean Field Game Perspective Jian Li Texas A&M University April 30 th, 2015 Jointly with R.

Incentivizing Sharing in Realtime D2D Streaming Networks: A Mean Field

Game Perspective

Jian LiTexas A&M University

April 30th, 2015

Jointly with R. Bhattacharyya, S. Paul, S. Shakkottai and V.

Subramanian

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Collaborative resource sharing systems are widespread, e.g. content sharing systems.

Bilateral exchange of utility: Bit-Torrent systems

tit-for-tat type strategies are feasible. Multilateral exchange: Societal Networks

more complex mechanisms are needed: Wireless content sharing using

broadcast D2D networks. How is an agent to determine whether

to collaborate with others, and whether it has received a fair compensation for its contribution?

Motivation

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Design mechanisms for cooperation in systems with repeated multilateral interactions.

Motivation (Cont’d)

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System Overview

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Timing Sequence and QoS

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Timing Sequence and QoS

Deficit Queue:

Quality of experience: (convex, monotone increasing)QoS Model adapted from work by Hou, Borkar & Kumar

(2009).

Random linear coding

Decode

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Timing Sequence and QoS

Allocation:Number of chunks transmitted by each agent:Deficit Evolution:

IID

RLC with large field size

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Lifetimes of the agents are geometrically distributed: An agent might quit at any time and a new agent takes its place: regeneration w.p .

Agents are mobile: randomly permute the agents in different clusters at each time. (static cluster also possible).

System Model

E.g. Stadium, concert or protest meeting

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Over all clusters of agents

No regeneration:

Regenerations:

Objective

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Goals: Mechanism that would incentivize

agents to truthfully revel their states: token scheme.

Allocation rule that optimizes the objective function, given truthful revelation: scheduling algorithm.

Android implementation of the system: music streaming app.

Objective(Cont’d)

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Mean Field Game

Think of a strategic game with continuum of opponents from the perspective of a particular agent (say 1).

The other agents are represented by a distribution over their states .

Chooses an action at each time so as to minimize its cost distribution over actions.

Mean field equilibrium: the stationary distribution of states should itself be .

Lastry & Lions (2007), Iyer, Johari & Sundararajan (2011) Manjrekar, Ramaswamy & Shakkottai (2014).

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Mean Field Model (Agent 1)

Decode or not

Stationary Distribution

.

B2D Arrivals

Transfer

Value from cluster viewValue from agent 1 view

Next state

Revealed state

RegenerationDistribution

Assumed future

distributionof other agents Revealed state

of other agents

Deficit cost

True state

Allocation

Mean Field Equilibrium

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Value From Cluster View

Decode or not

Stationary Distribution

.

B2D Arrivals

Transfer

Value from cluster viewValue from agent 1 view

Next state

Revealed state

RegenerationDistribution

Assumed future

distributionof other agents Revealed state

of other agents

Deficit cost

True state

Allocation

Optimal allocation from cluster’s viewpoint:

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Value from Agent 1 view

Decode or not

Stationary Distribution

.

B2D Arrivals

Transfer

Value from cluster viewValue from agent 1 view

Next state

Revealed state

RegenerationDistribution

Assumed future

distributionof other agents Revealed state

of other agents

Deficit cost

True state

Allocation

Optimal from agent 1’s view:

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Find an incentive compatible transfer scheme

that reconciles the two perceptions of value, and

an optimal allocation, assuming that an MFE exists.

Prove that an MFE exists, assuming that agents reveal states truthfully.

Proof Steps

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Suppose agents have some value function Let each agent get a payoff: Where is such that it maximizes

Will they reveal their true value? Yes. We can subtract any function of and

still retain truth-telling:

Traditional to set the reduction as the value of the system without agent i.

Generalized Grove’s Mechanism

Williams & Radner (1988), Bergemann & Valimaki (2010).

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Value function for agent 1 for arbitrary allocation :

Setting yields agent 1’s true value. Set the transfer (price charged) as

So the payoff to is

Groves Pivot Mechanism

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The allocation is to be chosen according to

Takes a very intuitive form. Example N = 8, T =4

System state: Calculate T – (N – ei)

Allocation

d1 = 2d2 = 3d3 = 1

4 – (8 – 4) = 0 4 – (8 – 5) = 1 4 – (8 – 2) = -2

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The allocation is to be chosen according to

Takes a very intuitive form. Example N = 8, T =4

Phase 1: 2 time slots

Allocation

d1 = 2d2 = 3d3 = 1

4 – (8 – 4) = 0 4 – (8 – 5) = 1 4 – (8 – 2) = -2

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The allocation is to be chosen according to

Takes a very intuitive form. Example N = 8, T =4

Phase 2: 1 time slot

Allocation

d1 = 2d2 = 3d3 = 1

4 – (8 – 4) = 0 4 – (8 – 5) = 1 4 – (8 – 2) = -2

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The allocation is to be chosen according to

Takes a very intuitive form. Example N = 8, T =4

Phase 3: 1 time slot

It is also easy to determine and the value functions through value iteration.

Allocation

d1 = 2d2 = 3d3 = 1

4 – (8 – 4) = 0 4 – (8 – 5) = 1 4 – (8 – 2) = -2

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The allocation is to be chosen according to

Allocation

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Transfers

Average transfer of 18039

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Custom kernel on Android to allow simultaneous 3G and WiFi. Allocation implemented through backoffs.

Implementation

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The price of B2D service is currently $10 per GB across many US cellular providers.

Consider music streaming at a rate of 250 kbps corresponding to our Android system.

Pure B2D: cost of spending 1000 seconds in the system is 31.25 cents.

Assume that if an agent experiences a deficit of 15 or above in a frame, it gets no payoff from that frame.

If each agent saves at least 11.26 cents, it has an incentive to participate in the D2D system.

Actual saving is 0.6 ∗ 31.25 = 18.75 cents (60% of the B2D costs) per agent.

Viability

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Conclusion

Designed an incentive framework to promote cooperation for collaborative systems.

Mean field model simplifies allocation, as well as value calculation: low complicity.

Implemented the system on Android devices and presented results illustrating its viability.

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Thank you!

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Appendix

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Truth-telling as dominant strategy Theorem: Our mechanism

is incentive compatible. The net payoff to agent i is

Properties of Mechanism

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Theorem: Our mechanism is individually rational, i.e., voluntary participation constraint is satisfied.

The net payoff to agent i is

Properties of Mechanism

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The above transfers are always positive.

Properties of Mechanism