Selfishness in packet forwarding/ Secure protocols for behavior - PowerPoint PPT Presentation

Selfishness in packet forwarding/ Secure protocols for behavior enforcement Security and Cooperation in Wireless Networks Georg-August University Göttingen

Part I: Selfishness in packet forwarding the operation of multi-hop wireless networks requires the nodes to  forward data packets on behalf of other nodes however, such cooperative behavior has no direct benefit for the  forwarding node, and it consumes valuable resources (battery) hence, the nodes may tend to behave selfishly and deny cooperation  if many nodes defect, then the operation of the entire network is  jeopardized question:  – When a node is requested to forward a packet by one of its neighbors, will it do so, if no mechanism enforces this cooperation behavior? Selfishness in packet forwarding/behavior enforcement Georg-August University Göttingen 2

Modeling packet forwarding as a game • Players: nodes • In each time slot t, each node I chooses a cooperation level m i (t) ϵ [0,1]; 0 represents full defection and 1 means full cooperation. • So mi(t) would represent the fraction of traffic routed through i at time t that i cooperatively forwards. • T S : constant amount of traffic sent by source S Strategy: cooperation level m C (1) m C (t) m C (0) time slot: time 0 1 t Benefit (of node i as the source on route r): proportion of packets sent by node i (as the source) on route r reaching their destination = the throughput experienced by i as a source  Selfishness in packet forwarding/behavior enforcement Georg-August University Göttingen 3

Benefit function benefit function : Experienced throughput : l       b S r t , T r ( ) m ( ) t s f k  k 1 where: s – source r – route on which s is a source t – time slot f k – forwarders for s m f k – cooperation level of forwarder f k b i – benefit function Example :       r t , T r ( ) m t ( ) m t ( ) A E C r (A →D ): A E C D m E (t) m C (t) T A Normalized throughput: Selfishness in packet forwarding/behavior enforcement Georg-August University Göttingen 4

Cost function Normalized throughput at forwarder f j : j      ˆ r t , m ( ) t where : r – route on which f k is a forwarder j f k t – time slot  k 1 f k – forwarders on route r m f k – cooperation level of forwarder f k where : Cost for forwarder f j on route r :     T s (r) – traffic sent by source s on route r      ˆ c r t , T r ( ) C r t , C – unit cost of forwarding f s j j (cost of forwarding one packet) Example : r (A →D ): A E C D m E (t) m C (t) T A        ˆ r t , m ( ) t m ( ) t m ( ) t C f E C k  k { , } E C          ˆ c r t , T r ( ) C r t , C A j Selfishness in packet forwarding/behavior enforcement Georg-August University Göttingen 5

Total payoff Payoff = Benefit - Cost              u t b q t , c r t , i i i   q S t ( ) r F t ( ) i i where: S i (t) – set of routes on which i is a source F i (t) – set of routes on which i is a forwarder The goal of each node is to maximize its total payoff over the game:       t  u t where: – discounting factor i t – time  t 0 Example :   u A (0) u A (1). u A (t). t Payoff: time slot: 0 1 t time Selfishness in packet forwarding/behavior enforcement Georg-August University Göttingen 6

Representation of the nodes as players y i Strategy function for node i :  i A -i where : x i  (r,t) – experienced throughput of route r at time t • Node i is playing against the rest of the network (represented by the box denoted by A -i ) • : strategy function of node I • The strategy of node I is defined by its strategy function and its initial cooperation level m i (0) • Node I chooses its strategy (cooperation level) at time t based on the normalized throughput it experienced in time slot t-1 on the route where it is a source Selfishness in packet forwarding/behavior enforcement Georg-August University Göttingen 7

Examples of strategies Initial Function cooperation  y  ( ) x Strategy i i i level   AllD (always defect) 0 i y ( ) 0 i   AllC (always cooperate) i y ( ) 1 1 i  y  1 y TFT (Tit-For-Tat) ( ) i i i (mimics the strategy of its opponent in the previous time slot) where y i stands for the input  non-reactive strategies : the output of the strategy function is independent of the input (example: AllD and AllC)  reactive strategies : the output of the strategy function depends on the input (example: TFT) Selfishness in packet forwarding/behavior enforcement Georg-August University Göttingen 8

Concept of dependency graph dependency: the benefit of each source is dependent on the behavior of its forwarders • Figure (a) shows a network with 5 routes • Figure (b) shows the correspondent dependency graph (an arrow from I to j means behavior of I has an effect on the benefit of j = I is an intermediate node for source j) dependency loop A Dependency loop L of node I is a sequence (I,v1),(v1,v2),…,(v(l -1),vl),(vl,i) of edges in the dependency graph. Selfishness in packet forwarding/behavior enforcement Georg-August University Göttingen 9

dependency loops  There exist two kinds of dependency loops: – Reactive dependency loop: • A dependency loop of I in which all nodes other than I play reactive strategies. – Non-Reactive dependency loop • A dependency loop of I in which all nodes other than I play non- reactive strategies.  It is interesting to find possible Nash equlibria of packet forwarding strategies – In such strategy profiles the nodes would be better off by cooperating Selfishness in packet forwarding/behavior enforcement Georg-August University Göttingen 10

Analytical Results (1/2) Theorem 1: If node i does not have Theorem 2: If node i has only non- any dependency loops, then its best reactive dependency loops, then its strategy is AllD. best strategy is AllD. node i node playing a non-reactive strategy   ( I ) 0 E other nodes   ( I ) 0 F Corollary 1: If every node plays AllD, it is a Nash-equilibrium. Selfishness in packet forwarding/behavior enforcement Georg-August University Göttingen 11

Analytical results (2/2) Theorem 3 (simplified): Assuming that node i is a forwarder, its best strategy will be to cooperate only if it has a dependency loop with each of its sources Corollary 2: If Theorem 3 holds for every node, it is a Nash-equilibrium. Example in which Corollary 2 holds: A B B A C C Dependency graph Network Selfishness in packet forwarding/behavior enforcement Georg-August University Göttingen 12

Classification of scenarios • A classification of scenarios from the cooperation perspective D: Set of scenarios, in which every node playing AllD is a Nash equilibrium • set of all possible scenarios (from Corollary 1 ) C: Set of scenarios, in which a Nash equilibrium based on cooperation is not excluded by Theorem 1 C2: Set of scenarios, in which cooperation is based on the conditions expressed in Corollary 2 Selfishness in packet forwarding/behavior enforcement Georg-August University Göttingen 13

Simulation settings Number of nodes 100, 150, 200 Distribution of the nodes random uniform Area size 1500x1500m, 1850x1850m, 2150x2150m Radio range 200 m Number of routes originating 1-10 at each node Route selection shortest path Number of simulation runs 1000 Selfishness in packet forwarding/behavior enforcement Georg-August University Göttingen 14

Simulation results • The scenarios in set C in the classification (see slide 13) • Result: the necessary condition expressed by theorem 1 is a strong requirement for cooperation in realistic settings (i.e. for a reasonably low no. of routes per node) Selfishness in packet forwarding/behavior enforcement Georg-August University Göttingen 15

Part I: Summary  Analytical results: – If everyone drops all packets, it is a Nash-equilibrium – In theory , given some conditions, a cooperative Nash-equilibrium can exist ( i.e., each forwarder forwards all packets )  Simulation results: – In practice , the conditions for cooperative Nash-equilibria are very restrictive : the likelihood that the conditions for cooperation hold for every node is extremely small  Consequences: – Cooperation cannot be taken for granted – Mechanisms that stimulate cooperation are necessary • incentives based on virtual currency • reputation systems Selfishness in packet forwarding/behavior enforcement Georg-August University Göttingen 16

Part II: Secure protocols for behavior enforcement  Motivation: Packet forwarding consumes resources – Nodes are rational => Maximize their own payoff – We have seen that cooperation does not happen naturally for packet forwarding in self-organized networks – Cooperation must be encouraged Provide incentive to cooperate within Routing and Forwarding protocols using a game theoretic approach Selfishness in packet forwarding/behavior enforcement Georg-August University Göttingen 17