Performance Analysis of Reputation-based Mechanisms for Multi-hop Wireless Networks

1. Performance Analysis of Reputation-based Mechanisms for Multi-hop Wireless Networks Fabio Milan Dipartimento di Elettronica Politecnico di Torino Turin, Italy Email: fabio.milan@polito.it Juan José Jaramillo and R. Srikant Coordinated Science Laboratory Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign Email: {jjjarami, rsrikant}@uiuc.edu

2. Outline • Problem Formulation • Cooperation without Collisions • Cooperation with Collisions • Performance Analysis CISS 2006, Princeton, NJ, USA

3. A B C Packet Forwarding +α –β • When B forwards a packet for A, node A gains α units and node B loses β units due to energy expenditure CISS 2006, Princeton, NJ, USA

4. Utility • α is the packet value • βis the transmission cost • pi is the dropping probability of node i • p-i is the dropping probability of the neighbor of node i ui =βpi–αp-i • βpiis the gain of dropping packets from the neighbor • αp-iis the loss for packets being dropped by the neighbor CISS 2006, Princeton, NJ, USA

5. Utility • Payoff of mutual cooperation0 • Payoff of mutual defectionβ – α • Packet value is greater than transmission cost • Mutual cooperation is preferable to mutual defection CISS 2006, Princeton, NJ, USA

6. It’s a Prisoner’s Dilemma • Each node drops all packets to maximize its utility • The Nash Equilibrium is pi*= p-i* = 1 • Individual selfishness leads to zero throughput • In multi-hop wireless networks, packet relaying requires cooperation • Need for mechanisms to sustain cooperation among selfish nodes CISS 2006, Princeton, NJ, USA

7. Incentives for Cooperation • Micro-payments • Reputation-based Mechanisms • End-to-end • Hop-by-hop • With Information Exchange • Without Information Exchange • Advantages • No Control Overhead • Collusion Resistance • Full Decentralization • Disadvantages • Performance Degradation due to Packet Collisions CISS 2006, Princeton, NJ, USA

8. Outline • Problem Formulation • Cooperation without Collisions • Cooperation with Collisions • Performance Analysis CISS 2006, Princeton, NJ, USA

9. Reputation-based Mechanism • Nodes take into account the effect of their actions on their future payoff • The weight of the k-th future payoff is δk • δ is the discount parameter 0≤δ≤1 • Nodes play a Repeated Game • δ is the probability to continue to play after each stage CISS 2006, Princeton, NJ, USA

10. Tit-for-tat • Cooperate on the first move, then do what the opponent did in the previous move pi(0) = 0 pi(k) = p-i(k-1) k > 0 CISS 2006, Princeton, NJ, USA

11. One-step Deviation • If both nodes cooperate, their payoff is 0. • Assume that node i deviates, by setting a dropping probability p>0 • Node i initially benefits from this deviation • As the neighbor reacts, node i suffers packet losses • Node i reacts to the punishment by punishing its neighbor • … • The discounted payoff of i in case of deviation is a function ofα, β,δ and p • If it is not greater than 0, then being the first to defect is not rational CISS 2006, Princeton, NJ, USA

12. Equilibrium • Deviation from Tit-for-tat is not profitable if • If δis sufficiently large, the outcome is mutual cooperation • If transmission cost is close to packet value, then cooperation emerges only if the users are farsighted or stay in the system for a very long time CISS 2006, Princeton, NJ, USA

13. Outline • Problem Formulation • Cooperation without Collisions • Cooperation with Collisions • Performance Analysis CISS 2006, Princeton, NJ, USA

14. B C D E A The Hidden Terminal is Back –α –β • When D forwards a packet from C to E, interference may prevent C to hear this transmission • C does not know if D is cooperating or not CISS 2006, Princeton, NJ, USA

15. Perceived Defection • Packet collisions with “hidden terminals” result in a distorted reputation • Estimate of neighbor’s dropping probability: either cannot “hear” neighbors transmission due to another neighbor’s transmission () or can hear and neighbor drops a relay packet CISS 2006, Princeton, NJ, USA

16. Generated Traffic ∞ λ Transit Traffic Dropped Traffic Queueing Model • The network load λ is independent of the dropping probabilitiesif • Infinite Backlog, no end-to-end Congestion Control • A node always transmits, within the MAC constraints: either it transmits its • own packet or a relay packet CISS 2006, Princeton, NJ, USA

17. Tit-for-tat • Cooperate on the first move, then do what you believe the opponent did in the previous move pi(0) = 0 CISS 2006, Princeton, NJ, USA

18. Retaliation • Due to collisions, simple Tit-for-tat is not sufficient to sustain cooperation 1 Tit-for-tat Perceived Defection λ 0 p 1 • Even if nodes initially cooperate, unjust punishment of perceived defection progressively leads to zero throughput CISS 2006, Princeton, NJ, USA

19. Generous Tit-for-tat • Add a tolerance threshold to mitigate throughput loss • The optimal tolerance to avoid both retaliation and exploitation is λ 1 Generous Tit-for-tat Perceived Defection λ 0 p 1 CISS 2006, Princeton, NJ, USA

20. Generous Tit-for-tat • Cooperate on the first move, then cooperate more than what you believe the opponent did in the previous move pi(0) = 0 CISS 2006, Princeton, NJ, USA

21. Equilibrium • Deviation from Generous Tit-for-tat is not profitable if • If δis sufficiently large, the outcome is mutual cooperation • Need an even larger δnow due to imperfect knowledge of neighbor’s actions CISS 2006, Princeton, NJ, USA

22. Outline • Problem Formulation • Cooperation without Collisions • Cooperation with Collisions • Performance Analysis CISS 2006, Princeton, NJ, USA

23. Game Parameters • λis a measure of the network load, if every node transmits at the same rate • δis a measure of the session length • If a session involves a great number of packets, it is reasonableto assume δ→ 1 • αis a measure of the information contained in a packet, with respect to the overall information flow transferred from source to destination • For a multimedia stream source, tolerant to packet losses, the packet value is small. For a file transfer source, the packet value is high. • βis a measure of the energy spent to transmit a packet, with respect to the total energy available to the node • For a terminal connected to the AC power, the transmission cost is low. For a terminal running out of battery, the transmission cost is high. CISS 2006, Princeton, NJ, USA

24. Throughput Upper Bound Throughput Cooperative Nodes Selfish Nodes 0 Offered Load • Beyond this critical threshold, nodes perceive no incentive to cooperate CISS 2006, Princeton, NJ, USA

25. 1/3 1/3 1/3 Packet Value Lower Bound • The capacity of a wireless network is limited (Gupta – Kumar, 2000) • If α is sufficiently large, there exists a value of δ that achieves cooperation for every feasible load CISS 2006, Princeton, NJ, USA

26. Conclusion • Developed a game-theoretic framework to evaluate the performance of hop-by-hop reputation-based mechanisms for multi-hop wireless network, in presence of packet collisions with “hidden terminals” • Explored the conditions for the emergence of cooperation in a network of selfish users, in terms of network load, session length, application type and energy constraints • Ongoing work: How does the network topology affects the conditions for the emergence of cooperation? • Ongoing work: Simulation experiments to study how the externalities introduced by an end-to-end congestion control affect the stability of the mechanism • As for now, our model suggests that if nodes use Skype™ while running out of battery, then they are unlikely to cooperate… CISS 2006, Princeton, NJ, USA

27. Thank You! CISS 2006, Princeton, NJ, USA