On Selfish Behavior in CSMA/CA Networks

On Selfish Behavior in CSMA/CA Networks Mario Čagalj1 Saurabh Ganeriwal 2 Imad Aad 1 Jean-Pierre Hubaux 1 1 LCA-IC-EPFL 2 NESL-EE-UCLA March 17, 2005 - IEEE Infocom 2005 -

Introduction CSMA/CA is the most popular MAC paradigm for wireless networks CSMA/CA protocols rely on a (fair) random deferment of packet transmission where nodes control their own random delays CSMA/CA is efficient if nodes follow predefined rules, however, nodes have a rational motive to cheat - IEEE Infocom 2005-1

Cheating pays well 8 7 Cheater Well-behaved cheater Throughput (Mbits/s) 6 5 4 3 2 1 well-behaved destination 0 0 2 4 6 8 10 12 14 16 Contention window of Cheater - IEEE Infocom 2005-2

Our goal Study the coexistence of a population of greedy stations Derive the conditions for the stable and optimal functioning of a population of greedy stations - IEEE Infocom 2005-3

Model and assumptions Network of N nodes (transmitters) out of which C are cheaters IEEE 802.11 protocol MAC layer authentication (no Sybil attack) single collision domain (no hidden terminals) nodes always have packets (of the same size) to transmit Contention window size-based cheating fix W i = W min = W max (no exponential backoff) delay transmissions for d i U {1, 2,..., W i } Cheaters are rational (maximize their throughput r i ) - IEEE Infocom 2005-4

Cheaters utility function U i Derived from Bianchi s model of IEEE 802.11 each cheater i controls its access probability τ i = 2 W i + 1 cheater i receives the following throughput: U i (τ i, τ i ) r i (τ i, τ i ) = τ i c i 1(τ i ) τ i c i 2 (τ i) + c i 3 (τ i), where τ i (τ 1,..., τ i 1, τ i+1,..., τ N ). - IEEE Infocom 2005-5

Static CSMA/CA game Static games players make their moves independently of other players players play the same move forever A move in the CSMA/CA game corresponds to setting the value of the cheater s contention window W i (that is, τ i ) Solution concept - Nash equilibrium (NE) W = (W 1, W 2,..., W C ) is a NE point if i = 1,..., C, we have: U i (W i, W i ) U i (Ŵi, W i ), Ŵi {1, 2,..., W max } - IEEE Infocom 2005-6

Nash equilibria of the static game Proposition 1. A vector W = (W 1,..., W C ) is a Nash equilibrium if and only if i {1, 2,..., C} s.t. W i = 1. Proposition 2. The static CSMA/CA game admits exactly W C max (W max 1) C Nash equilibria. Two families of Nash equilibria define D {i : W i = 1, i = 1, 2,..., C} 1st family, D = 1, implying that only one cheater receives a non-null throughput (some allocations are Pareto-optimal!) 2nd family, D > 1, implying r i = 0, for i = 1,..., C (known as the tragedy of the commons) - IEEE Infocom 2005-7

How to avoid undesirable equilibria? Multiple Nash equilibria that are either highly unfair or highly inefficient

How to avoid undesirable equilibria? Multiple Nash equilibria that are either highly unfair or highly inefficient To derive a better solution we use Nash bargaining framework solve the following problem max C i=1 (r i r 0 i ) Π 1 : s.t. r R r r 0. where R is a finite set of feasible solutions, and r 0 i max i min i r i, i = 1, 2,..., C is the disagreement point - IEEE Infocom 2005-8

Uniqueness, fairness and optimality Π 1 admits a unique, fair and Pareto-optimal solution W (Nash bargaining solution) 1.2 Throughput (Mbits/s) 1 0.8 0.6 0.4 0.2 0 Nash-equilibrium point Pareto-optimal point Simulations Analytical 0 10 20 W* 30 40 50 60 70 80 90 100 Contention window (W) of greedy stations - IEEE Infocom 2005-9

Dynamic CSMA/CA game W is a desirable solution, but is not a Nash equilibrium i.e., W i > 1, i = 1,..., C

Dynamic CSMA/CA game W is a desirable solution, but is not a Nash equilibrium i.e., W i > 1, i = 1,..., C In the model of dynamic games cheaters utility function changes to J i = r i P i, where P i is a penalty function cheaters are reactive - IEEE Infocom 2005-10

Penalty function P i Proposition 3. Define: P i = { pi, if τ i > τ 0, otherwise, where p i / τ i > r i / τ i and τ i < 1, i = 1, 2,..., C. Then, J i = r i P i has a unique maximizer τ. - IEEE Infocom 2005-11

Graphical interpretation Example: P i = k i (τ i τ), with k i > r i / τ i 0.4 0.3 Nash equilibrium point P i r i normalized payoff 0.2 0.1 J i = r i P i 0-0.1 0 0.05 0.1 0.15 0.2 i - IEEE Infocom 2005-12

Making W a Nash equilibrium point Let τ = min τ i, (i.e., W = i=1,...,c max W i) i=1,...,c Each player j calculates a penalty p j i given that r i > r j, as follows: to be inflicted on player i j, p j i = r i r j note, r i / τ i > 0 and r j / τ i < 0 p j i / τ i > r i / τ i hence, J i = r i p j i = r j has a unique maximizer τ i = τ j

Making W a Nash equilibrium point (cont.) Moving Nash Equilibrium 1.2 Throughput (Mbits/s) 1 0.8 0.6 0.4 0.2 0 Pareto-optimal Nash equilibrium Nash-equilibria Simulations Analytical 0 10 20 W* 30 40 50 60 70 80 90 100 Contention window (W) of greedy stations - IEEE Infocom 2005-14

Implementation of the penalty function Achieved by selective jamming Penalty should result in r i = r j, therefore T jam = (r i /r j 1)T obs Throughput (Mbits/s) 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 Cheater X Other cheaters 0 50 100 150 200 250 Time (s) Throughput of cheater X (Mbits/s) 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 With jamming Without jamming Unique maximizer for cheater X 0 10 20 30 40 50 60 Contention window (W X ) of cheater X - IEEE Infocom 2005-15

Adaptive strategy Prescribes to a player what to do when the player is penalized (jammed) Throughput (Mbits/s) 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 Cheater X Other cheaters 0 50 100 150 200 250 300 350 400 450 500 Contention window size 35 30 25 20 15 10 Cheater X 5 Other cheaters 50 100 150 200 250 300 350 400 450 500 Time (s) Time (s) - IEEE Infocom 2005-16

Fully distributed algorithm Evolution of the contention windows and the aggregated cheaters throughput for N = 20, C = 7, the step size γ = 5 30 30 Contention window size 25 20 15 10 5 0 Ch. X: Distrib. prot. Ch. Y: Distrib. prot. Ch. X, Y: Forced CW 160 180 200 220 240 260 280 300 320 Contention window size 25 20 15 10 Our protocol stops at this point 5 Ch. 1-7: Distributed prot. 0 Ch. 1-7: Forced CW 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 Time (s) Aggregated throughput of cheaters (Mbits/s) - IEEE Infocom 2005-17

Conclusions Static CSMA/CA game admits two families of Nash equilibria one family includes equilibria that are also Pareto-optimal Nash bargaining framework is appropriate to study fairness at the MAC layer using this framework we have identified the unique Pareto-optimal point exhibiting efficiency and fairness We have shown how to make this Pareto-optimal point a Nash equilibrium point, by providing a fully distributed algorithm that leads a population of greedy stations to the efficient Paret-optimal Nash equilibrium