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. Bhattacharyya, S. Paul, S. Shakkottai and V. Subramanian 1
Jan 11, 2016
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
1
2
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
3
Design mechanisms for cooperation in systems with repeated multilateral interactions.
Motivation (Cont’d)
4
System Overview
5
Timing Sequence and QoS
6
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
7
Timing Sequence and QoS
Allocation:Number of chunks transmitted by each agent:Deficit Evolution:
IID
RLC with large field size
8
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
9
Over all clusters of agents
No regeneration:
Regenerations:
Objective
10
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)
11
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).
12
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
13
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:
14
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:
15
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
16
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).
17
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
18
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
19
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
20
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
21
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
22
The allocation is to be chosen according to
Allocation
23
Transfers
Average transfer of 18039
24
Custom kernel on Android to allow simultaneous 3G and WiFi. Allocation implemented through backoffs.
Implementation
25
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
26
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.
27
Thank you!
28
Appendix
29
Truth-telling as dominant strategy Theorem: Our mechanism
is incentive compatible. The net payoff to agent i is
Properties of Mechanism
30
Theorem: Our mechanism is individually rational, i.e., voluntary participation constraint is satisfied.
The net payoff to agent i is
Properties of Mechanism
31
The above transfers are always positive.
Properties of Mechanism