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

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 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 view Value from agent 1 view Next state Revealed state Regeneration Distribution Assumed future distribution of 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 view Value from agent 1 view Next state Revealed state Regeneration Distribution Assumed future distribution of 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 view Value from agent 1 view Next state Revealed state Regeneration Distribution Assumed future distribution of 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 – e i ) Allocation d 1 = 2 d 2 = 3 d 3 = 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 d 1 = 2 d 2 = 3 d 3 = 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 d 1 = 2 d 2 = 3 d 3 = 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 d 1 = 2 d 2 = 3 d 3 = 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 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 cents, it has an incentive to participate in the D2D system.  Actual saving is 0.6 ∗ = 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