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. March 22, 2006CISS 2006, Princeton, NJ, USA2 Outline Problem Formulation Cooperation without Collisions Cooperation with Collisions Performance Analysis

3. March 22, 2006CISS 2006, Princeton, NJ, USA3 Packet Forwarding ABC +α+α–β–β When B forwards a packet for A, node A gains α units and node B loses β units due to energy expenditure

4. March 22, 2006CISS 2006, Princeton, NJ, USA4 Utility u i = βp i – αp -i α is the packet value β is the transmission cost p i is the dropping probability of node i p -i is the dropping probability of the neighbor of node i βp i is the gain of dropping packets from the neighbor αp -i is the loss for packets being dropped by the neighbor

5. March 22, 2006CISS 2006, Princeton, NJ, USA5 Utility Payoff of mutual cooperation0 Payoff of mutual defectionβ – α Packet value is greater than transmission cost Mutual cooperation is preferable to mutual defection

6. March 22, 2006CISS 2006, Princeton, NJ, USA6 It’s a Prisoner’s Dilemma Each node drops all packets to maximize its utility The Nash Equilibrium is Individual selfishness leads to zero throughput In multi-hop wireless networks, packet relaying requires cooperation Need for mechanisms to sustain cooperation among selfish nodes p i * = p -i * = 1

7. March 22, 2006CISS 2006, Princeton, NJ, USA7 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

8. March 22, 2006CISS 2006, Princeton, NJ, USA8 Outline Problem Formulation Cooperation without Collisions Cooperation with Collisions Performance Analysis

9. March 22, 2006CISS 2006, Princeton, NJ, USA9 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 δ k δ is the discount parameter 0 ≤ δ ≤ 10 ≤ δ ≤ 1 Nodes play a Repeated Game δ is the probability to continue to play after each stage

10. March 22, 2006CISS 2006, Princeton, NJ, USA10 Tit-for-tat Cooperate on the first move, then do what the opponent did in the previous move p i (0) = 0 p i (k) = p -i (k-1) k > 0

11. March 22, 2006CISS 2006, Princeton, NJ, USA11 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 of α, β, δ and p If it is not greater than 0, then being the first to defect is not rational

12. March 22, 2006CISS 2006, Princeton, NJ, USA12 Equilibrium Deviation from Tit-for-tat is not profitable if If δ is 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

13. March 22, 2006CISS 2006, Princeton, NJ, USA13 Outline Problem Formulation Cooperation without Collisions Cooperation with Collisions Performance Analysis

14. March 22, 2006CISS 2006, Princeton, NJ, USA14 The Hidden Terminal is Back BCDE – α– α–β–β A 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

15. March 22, 2006CISS 2006, Princeton, NJ, USA15 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

16. March 22, 2006CISS 2006, Princeton, NJ, USA16 Queueing Model λ Dropped Traffic ∞ Generated Traffic Transit Traffic 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 The network load λ is independent of the dropping probabilities if

17. March 22, 2006CISS 2006, Princeton, NJ, USA17 Tit-for-tat Cooperate on the first move, then do what you believe the opponent did in the previous move p i (0) = 0

18. March 22, 2006CISS 2006, Princeton, NJ, USA18 Retaliation Due to collisions, simple Tit-for-tat is not sufficient to sustain cooperation p 0 1 1 λ Tit-for-tat Perceived Defection Even if nodes initially cooperate, unjust punishment of perceived defection progressively leads to zero throughput

19. March 22, 2006CISS 2006, Princeton, NJ, USA19 Generous Tit-for-tat p 0 1 1 λ Perceived Defection Add a tolerance threshold to mitigate throughput loss The optimal tolerance to avoid both retaliation and exploitation is λ

20. March 22, 2006CISS 2006, Princeton, NJ, USA20 Generous Tit-for-tat p i (0) = 0 Cooperate on the first move, then cooperate more than what you believe the opponent did in the previous move

21. March 22, 2006CISS 2006, Princeton, NJ, USA21 Equilibrium Deviation from Generous Tit-for-tat is not profitable if If δ is sufficiently large, the outcome is mutual cooperation Need an even larger δ now due to imperfect knowledge of neighbor’s actions

22. March 22, 2006CISS 2006, Princeton, NJ, USA22 Outline Problem Formulation Cooperation without Collisions Cooperation with Collisions Performance Analysis

23. March 22, 2006CISS 2006, Princeton, NJ, USA23 Game Parameters λ is a measure of the network load, if every node transmits at the same rate δ is a measure of the session length –If a session involves a great number of packets, it is reasonable to assume δ → 1 α is 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. β is 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.

24. March 22, 2006CISS 2006, Princeton, NJ, USA24 Throughput Upper Bound 0 Cooperative Nodes Selfish Nodes Throughput Offered Load Beyond this critical threshold, nodes perceive no incentive to cooperate

25. March 22, 2006CISS 2006, Princeton, NJ, USA25 Packet Value Lower Bound 1/3 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

26. March 22, 2006CISS 2006, Princeton, NJ, USA26 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…

27. March 22, 2006CISS 2006, Princeton, NJ, USA27 Thank You!