A Decision A Decision A Decision-Analytic Approach for A Decision Analytic Approach for Analytic Approach for Analytic Approach for P2 2P Cooperation Policy Setting P Cooperation Policy Setting p p y y g g G G. V k l 1 Th G P Vakili 1 , Th. G. Papaioannou 2 , S. Khorsandi 1 2 S Kh d 1 1 Amirkabir University of Technology Tehran Iran Tehran – Iran 2 Ecole Polytechnique Fédérale de Lausanne (EPFL) Lausanne – Switzerland NetEcon’10
O tli O tli Outline Outline � Our Motivation & Goal � Our Approach � Our Approach � System Model � Decision-Analytic Approach � Analysis � Analysis � NE Analysis � Evaluation � Conclusion Conclusion 2
O O Our Motivation & Goal Our Motivation & Goal M ti M ti ti ti & G & G l l � Overall performance of P2P systems depends on resource contributions of individual peers. � Rational peers decide on their cooperation policies according to their individual utilities according to their individual utilities. � Inherent conflict among individual utilities of the rational � Inherent conflict among individual utilities of the rational peers results in � free-riding � unfair contribution � low participation � Our goal is dealing with the inherent individual utility conflicts to improve overall performance of the system conflicts to improve overall performance of the system. 3
Our Approach Our Approach Our Approach Our Approach � We employ decision-theory to model cooperation p y y p policy setting of participating peers: � Each peer chooses its strategy according to observable strategies of the other peers. � Through a swarm-based iterative learning process: � Rational peers set their cooperation policies so as to R l h l maximize their own utility. � Their decisions are coordinated in a distributed manner to Their decisions are coordinated in a distributed manner to improve the social welfare of the system. � The game-theoretic analysis lacks an explicit and tractable handling of the individual strategy g gy dynamics present in the interactions among individual peers p 4
SYSTEM MODEL SYSTEM MODEL SYSTEM MODEL SYSTEM MODEL 5
Individual Individual- -based Lagrangian based Lagrangian Swarm Swarm Model Model � Interacting participants of a P2P system exhibit general I t ti ti i t f P2P t hibit l properties of an individual based Lagrangian swarm model: model: � composed of many individual peers; � the interactions are based on local information exchange; g ; � emergence; � self-organization. � We made two modifications to adopt this model in the context of a P2P system: h f P2P � Distributed local objectives (utility functions) are defined for individual peers individual peers. � The interaction of particles is represented as a non- cooperative game. 6
Definitions Definitions Definitions Definitions � We assume that N peers p ; i:1 � We assume that N peers p i ; i:1,…,N participate in N participate in the system � Policy ( d i ) P li ( d ) � a peer’s policy is its level of cooperation (a numerical assessment of the peer’s contributed resources to the t f th ’ t ib t d t th system) � Strategy ( s i ) St t ( ) � the strategy of a peer reflects its decision on the change i it in its cooperation level (policy) ti l l ( li ) � Utility ( U i ) � A peer's utility is determined by its strategy choices and depends on several parameters - discussed as follows. 7
Utility Function Utility Function Utility Function Utility Function � Cost and Benefit � the total cost for participating in the system with cooperation level of d i will be c i d i � the benefit of cooperation of p j to p i is represented by b ij d j ; where b ij is measured (e.g.) as the inverse of latency ( g ) y ij j ij � Incentives for high contribution � Incentives for high contribution � it is modeled by a monotonically increasing function of the cooperation policy of a peer p i , denoted by bc i h i li f d d b b � Utility: ∑ ∑ = − ≡ U bc . b . d c d ; ; b 0 i i i i ij ij j j i i i i ii ii ∈ j N 8
DECISION DECISION-ANALYTIC DECISION DECISION ANALYTIC ANALYTIC ANALYTIC APPROACH APPROACH 9
O O Overall Overall ll ll � Observable strategies of other peers are monitored by each peer in a sequence of iterations. p q � Based on this empirical evidence each peer can decide � Based on this empirical evidence, each peer can decide rationally on a strategy in every iteration. � This chain of decisions are made based on a method inspired by particle swarm optimization (PSO). i i d b ti l ti i ti (PSO) � Through this chain of decisions each participating peer concludes its final cooperation policy with respect to the other peers' behavior. 10
M More Formally More Formally M F F ll ll � T o maximize its expected utility U i , each peer p i sets its final cooperation policy through an iterative decision making process: k � p i monitors the strategies of the other peers in its neighborhood N locally and evaluates their strategies N i locally and evaluates their strategies. next in the next iteration with respect to � It chooses its strategy s i the evaluation result and to its own experience: = + − + − s next s current r c ( d d current ) r c ( d d current ) i i 1 1 p i 2 2 n i � d p is the best previous policy of p i and d n denotes the best policy d i h b i li f d d d h b li of the other peers in N i . � Then the cooperation policy d i of peer p i is revised as follows: = = + + d d next d d current s s next i i i 11
ANALYSIS ANALYSIS - ANALYSIS ANALYSIS EVALUATION EVALUATION 12
NE A NE Analysis NE Analysis NE A l l i i � We employ Nash equilibrium analysis to investigate the predicted strategies for the participating peers by th d the decision-analytic approach. i i l ti h � According to [Buragohain et al. P2PComputing03] for a A di [B 03] f h i l P2PC i similar quantitative model of the system in a homogeneous setting (for all p i b ij = b c i = c) the NE is homogeneous setting (for all p i ,b ij b, c i c), the NE is given by: = − − ± ± − − − d d * * ( ( b b ( ( N N 1 1 ) ) / / 2 2 c 1 1 ) ) (( (( b b ( ( N N 1 1 ) ) / / 2 2 c 1 1 ) ) 2 2 1 1 ) ) 1 1 / / 2 2 � As we numerically show: y � The expected NE of the game is not the Pareto-optimal one. � The outcome derived from the proposed decision-analytic approach would make all players better-off. h ld k ll l b ff 13
The comparison of the average The comparison of the average p p g g cooperation level cooperation level 9 8 evel 7 7 operation L 6 5 4 4 Average Coo Hetero 3 Homo 2 NE NE 1 1 A 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Scaled Benefit � Tendency toward Pareto efficiency Tendency toward Pareto efficiency � Better outcome than NE � Both homogeneous and heterogeneous settings evolve Both homogeneous and heterogeneous settings evolve similarly 14
Convergence to a set of Pareto Convergence to a set of Pareto g efficient strategy efficient strategy 9 8 8 l ation Leve 7 6 age Coopera 5 5 4 3 Scaled Benefit = 0.05 Avera 2 Scaled Benefit = 0.5 1 Scaled Benefit = 1 0 1 6 11 16 21 26 31 36 41 46 Number of Iterations � Fast convergence regardless of the target cooperation level 15
CONCLUSION CONCLUSION CONCLUSION CONCLUSION 16
C C Conclusion Conclusion – Future Work l l i i F t F t Future Work W W k k � We propose a decision-analytic approach based on the modified swarm model, to set and coordinate rational decisions of the individual peers on their cooperation policies in a distributed individual peers on their cooperation policies in a distributed manner. � The resulting cooperation policies constitute the final set of decisions that maximize rational peers' utility in-line with the social welfare of the system. y � Incentive-compatible for peers to follow � Our approach quickly approximates a Pareto-optimal operating point of the system. � In our future work, we will investigate information exchange mechanisms that involve incentives for neighbor truthfulness or own observation and verification. 17
THANK THANK YOU FOR YOU FOR YOUR YOUR ATTENTION. ATTENTION. MORE QUESTIONS MORE QUESTIONS TO: TO: Golnaz Vakili g_vakili@aut.ac.ir Distributed Information Systems Lab, EPFL http://lsir.epfl.ch 18
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