IEEE/ACM TRANSACTIONS ON NETWORKING 1 Social Norm...

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IEEE/ACM TRANSACTIONS ON NETWORKING 1

Social Norm Incentives for NetworkCoding in MANETs

Chuchu Wu, Mario Gerla, Fellow, IEEE, and Mihaela van der Schaar, Fellow, IEEE

Abstract— The performance of mobile ad hoc networktransmissions subject to disruption, loss, interference, andjamming can be significantly improved with the use of networkcoding (NC). However, NC requires extra work for forwarders,including additional bandwidth consumption due to transmittingoverheads for redundant NC packets and additional processingdue to generating the NC packets. Selfish forwarders may preferto simply forward packets without coding them to avoid suchoverhead. This is especially true when network coding mustbe protected from pollution attacks, which involves additional,often processor intensive, pollution detection procedures.To drive selfish nodes to cooperate and encode the packets,this paper introduces social norm-based incentives. The socialnorm consists of a social strategy and a reputation systemwith reward and punishment connected with node behavior.Packet coding and forwarding are modeled and formalizedas a repeated NC forwarding game. The conditions for thesustainability (or compliance) of the social norm are identified,and a sustainable social norm that maximizes the social utility isdesigned via selecting the optimal design parameters, includingthe social strategy, reputation threshold, reputation updatefrequency, and the generation size of network coding. For thisgame, the impacts of packet loss rate and transmission patternson performance are evaluated, and their impacts on the decisionof selecting the optimal social norm are discussed. Finally,practical issues, including distributed reputation disseminationand the existence of altruistic and malicious users, are discussed.

Index Terms— Game theory, network coding, incentive design,reputation scheme.

I. INTRODUCTION

MOBILE devices like smart phones and tablets arebecoming increasingly powerful and capable to func-

tion not only as clients, but also as peers in a fully fledgedad hoc network. For instance, at a sports arena a spectatormay capture a scene on video from a vantage point and peer-to-peer broadcast the video stream to other spectators withan obstructed view. Similarly, a mobile may propagate toneighbors in ad hoc mode a stream that it is downloading fromthe Internet via WiFi or 3G. The mobile devices, however, haveenergy constraints. Since forwarding other devices’ packetsprovides no benefit to a mobile that is not an intended desti-nation, rather, it consumes battery resources, a self-interested

Manuscript received February 25, 2015; revised December 1, 2015 andSeptember 3, 2016; accepted December 26, 2016.; approved by IEEE/ACMTRANSACTIONS ON NETWORKING Editor A. Markopoulou.

C. Wu is with Teradata Corporation, El Segundo, CA 90245 USA (e-mail:[email protected]).

M. Gerla is with the Department of Computer Science, University of Califor-nia at Los Angeles, Los Angeles, CA 90095 USA (e-mail: [email protected]).

M. van der Schaar is with the Department of Electrical Engineering,University of California at Los Angeles, Los Angeles, CA 90095 USA(e-mail: [email protected]).

Digital Object Identifier 10.1109/TNET.2017.2656059

relay node chooses not to forward the packets. If every relaynode drops others’ packets, the video never gets deliveredto friends several hops away. This selfish behavior, however,can backfire. When the selfish node transmits its own videofile, it will be treated the same way, i.e., its file will bedropped. This behavior is known as “tit for tat” in cooperativeP2P distribution protocols (e.g. bit torrent) and is actually aprimitive type of incentive to induce rational peers to cooperateand serve each other.

A similar situation occurs when the video stream is networkcoded. Network coding [1]–[3] has been shown to improvestreaming performance dramatically in disruptive wirelessnetworks with random loss, jamming or external interference.When the video originator streams the data to one or morereceivers in a peer-to-peer ad hoc network, where the linksbetween intermediate nodes can be stressed with high loss rate,network coding can be used to generate redundant packets andoffset the loss. Without coding, the linear forwarding schemefails. It does not retransmit lost packets, due to the broadcastMAC used for multicast streaming. Hence network coding isbeneficial to improve packet delivery rate and stream quality.

While network coding has numerous benefits in thesedeployment scenarios, it also introduces extra costs for theinterim forwarders. Comparing with simply forwarding thepackets, when network coding is applied with redundancyintroduced to offset the wireless loss, the intermediate nodesneed to transmit more packets, which results in more band-width and power consumptions. Selfish intermediate nodesare motivated to avoid the extra costs and thus, will notperform NC.

Network coding is susceptible to pollution attacks. Uponreceiving corrupted packets, the destination cannot decode andmust throw away all the encoded packets in the generation.So network coding streams must be protected by specialtechniques that reveal the presence of an attack and allow todiscard faulty packets. Such pollution protection mechanismsintroduce even more costs for the intermediate forwarders,which motivates their selfish behavior. Even though there existlight-weight secure schemes, they have other issues, which wewill discuss extensively in the related work.

Due to the potentially high cost of secure (i.e. pollutionprotected) network coding with respect to simple forwarding,selfish intermediate nodes are more likely to refuse to performcoding in order to save power for their own future trans-missions. Hence, an incentive scheme is needed to encour-age intermediate nodes to perform secure network coding.Incentive schemes have been proposed for conventional mobilenetworks before, e.g. [25]–[36]. In this paper we extend those

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2 IEEE/ACM TRANSACTIONS ON NETWORKING

schemes to the network coding scenario. We must qualify thedefinition of secure network coding to refer strictly to thepollution detection capability. Accordingly, only the cost ofdetection is considered in the game setting. There are in factother costs that add to the basic detection, namely reliablereputation accounting, collusion prevention, malicious attacksto reputation, etc. These issues must be definitely addressed inthe implementation and the related costs must be eventuallyincluded in the model. However, the inclusion of these factors,when known with precision, will not alter the basic structureand the main conclusions on this study, which rest on theassumption that “secure” network coding is more expensivethan simple packet forwarding.

In summary, streaming in lossy ad hoc networks greatlybenefits from network coding; network coding must be pro-tected from pollution; pollution protection takes a heavy toll onprocessing overhead and battery consumption, inviting selfishbehavior by intermediate nodes; this in turn defies networkcoding. Even worse, selfish nodes can drop the packets tosave transmission costs, and thus cause more severe damageto network performance. It is thus apparent that to break thisimpasse and jump start network coding among coding capablenodes or at least forwarding among coding incapable nodes,an incentive mechanism is essential. The main purpose of thispaper is to present an efficient incentive scheme for networkcoding.

To maintain the model analytically tractable, for the firstpart of this paper we assume a rather simple topology scenario,with unicast from a source to a destination via a single interme-diate. The model can be extended to multi-hop and multicastscenarios. With the unicast session, the source node injects anetwork coded stream. The intermediate node may carry outnetwork coding or may opt to simply forward, or even drop thepackets, either because it cannot perform coding, or becauseit wants to avoid the network coding processing overhead andthus energy expenditure, an important consideration in mobiledevices. The social norm based incentive scheme we proposeprescribes the intermediate nodes to perform coding and injectredundant packets. If the receiver detects non-compliance bythe intermediate node (i.e., the intermediate node refuses toinject redundant coded packets in presence of loss), it willbroadcast the deviating action to a scoped neighborhood andthe intermediate node’s reputation will be lowered. As aconsequence, when a low reputation intermediate node in turnbecomes source and sends its own stream, it will be punished;namely, the neighbors will refuse to code its packets accordingto social strategy. This “punishment” should be sufficient topersuade the nodes that are frequent video originators orreceivers to encode the packets, if they can.

The above topology is extremely simple. However, thecareful reader will notice that the method and the results of thissimple topology can be extended to much more general andcomplex topologies with multiple intermediate hops, multiplepaths and multiple receivers (i.e., broadcast), as discussed laterin this paper.

When multiple streams are downloaded from differentsources, the possibility of inter-flow network coding arises.Inter-flow network coding can offer additional throughput

benefits above intra-flow network coding. It is however anorthogonal problem, for two reasons. First, inter-flow codingdoes not improve the reliability in conditions of heavy inter-ference and connectivity intermittence (as is the case here).Secondly, inter-flow network coding introduces neither extraprocessing overhead nor extra pollution risks. So, nodes donot need extra incentives to implement it when it is cost-effective. For these reasons we do not consider inter-flowcoding.

II. RELATED WORK

A. Secure Network Coding Schemes for Pollution Protection

Several methods have been proposed for NC pollutionavoidance, but they all introduce extra overheads to theintermediate forwarders. The most popular method is thehomomorphic hash/signature [4], [5]. This method howeverrequires heavy processing overhead, up to 100 times theprocessing of conventional network coding [3]. There are othermethods that are less processor consuming. For example, theanti pollution schemes DART [40], Null keys [41] and SplitNull Keys [42] significantly reduce the NC security overheadwith respect to Homomorphic signature/hashing. However,these schemes introduce either latency or processing overheadissues of their own that must be accounted for before adoption.DART requires node synchronization which is difficult toapply to a dynamic MANET where nodes join and leave overtime. Also, there is a latency between the reception of a datablock and the reception of the checksum that verifies it. Forreal-time applications that are sensitive to delays, this latencycan cause unacceptable quality degradation. Talooki et al. alsopointed out this issue in the survey that investigates existingsecure network coding schemes [43]. Null Keys is an elegantscheme. However, it requires that for each generation the NullKey matrix is propagated to the network using a homomorphicscheme. Thus, the overhead is reduced with respect to thescheme that Homo-encodes all data packets. However, thereis still significant overhead especially if generations are small,say 8 packets, as required for real time streaming. Moreover,there is non-negligible latency required to distribute the NullKey before beginning the transmission of generation packets,as analyzed in [43]. Split Null Key improves upon NullKey in the following way. The Null Key is the sum of twosubkeys: a generation independent random subkey that mustbe delivered to trusted forwarders before the application starts.if it is captured by malicious nodes, the system fails. Then,the generation dependent subkey is broadcast to everyone (noneed to secure it). This scheme highly relies on the trustedforwarders at the beginning, which however is not feasiblefor fully distributed and dynamic mobile ad hoc networkswhere no one is guaranteed to be trusted. This issue is alsopointed out in [43]. In summary, DART introduces latencyand thus is not feasible for time sensitive applications such asvideo streaming of live events such as sports events, concertsand vehicular applications. Null Keys introduces softwarecomplexity and overhead to the point that some node may alsobe motivated to avoid. Split Null Keys also implies the cost ofsecure distribution of random Split Key, suggesting the use of


WU et al.: SOCIAL NORM INCENTIVES FOR NETWORK CODING IN MANETs 3

a game to incentivize, and also has problem in finding trustedforwarders for the initial distribution of subkeys. Hence, giventhat the motivation of selfish nodes in avoiding secure NC isstill valid, incentives are needed no matter what anti-pollutiontechnique is used.

B. Game Theoretic Research for Network Coding

There are related literatures [7]–[11] using game theory as atool to solve Network Coding problems, however those worksare very different from ours in the following aspects:

• The nodes or players in their models are not truly“selfish”. Even if the word “selfish” is often used todescribe the nodes or players in these literatures, nodesare only selfish in the sense that they take the actionto maximize its individual utility function, but the utilityfunction is designable by protocol designers. So the nodesare in fact puppets performing the predefined optimizedactions. However in our scheme, the utility functionsrepresent the users’ own benefits and costs that cannot bedesigned by protocol designers. Namely, nodes are trulyselfish, and games here are used to model their behaviors,as opposed to an optimization method in these relatedworks.

• The nodes in their model are obliged to performNetwork Coding as a common bottom line. However inour scheme, nodes are completely selfish users who areable to decline Network Coding in order to avoid costs.

• Existing game theoretic research on network codingconsiders only inter-flow network coding but not intra-flow network coding. So the actions in their games areeither bandwidth/rate allocation strategies [7]–[9] or routeselections [10], [11]. Differently, we consider intra-flownetwork coding, so the actions in our game are decisionsmade by intermediate nodes on whether performing intra-flow NC or not, or even dropping the packets.

Essentially, existing game theoretic research on networkcoding solve optimization problems among altruistic nodesinstead of handling selfish behavior.

C. Related Work in Incentive Design

There are two ways to deal with selfish behavior: detectand block the selfish users, or incentivize selfish users tocooperate. Schemes like watchdog and pathrater [13], as wellas a reputation scheme [14], have been proposed to detect andisolate selfish users in wireless networks, however if selfishbehavior becomes mainstream or pervasive, isolating selfishusers cannot be the ultimate solution.

There are related works designing incentives for selfishusers in different types of networks, which can be summa-rized as Table.I. The earliest incentive schemes come fromeconomics and are designed for human networks where usersare naturally selfish, e.g. online trading systems like eBay [16].Then incentives are introduced to peer-to-peer file sharingsystems where selfish behavior of peers can seriously degradethe system performance [17]–[24]. Up to here, trading orsharing problems are dominantly modeled as simple binary

TABLE I

RELATED WORKS ON INCENTIVE DESIGN FOR SELFISH USERS

action games, i.e., players have only two possible actions:{Serve, NotServe} or {Share, NotShare}. Such relativelysimple games are rigorously formalized and thoroughly ana-lyzed, various types of incentives (bartering, token, reputation)are explored, and solutions are optimized with the considera-tion of many practical factors.

Similarly, wireless networks can also be seriously affectedby selfish behaviors, e.g. dropping others’ packets to saveits own battery and bandwidth, and it can also be modeledas a simple binary action game for conventional wirelessnetworks without Network Coding, i.e., nodes can only chooseto either forward or drop the packets. Yet different fromthe sharing/trading systems where centralized credit/reputationschemes can be feasible, it is very hard to maintain a central-ized control scheme in wireless ad hoc networks. A limitedamount of work has been done to design incentives for con-ventional wireless networks [25]–[36]. Among them, only [26]aims at maximizing the overall utility of the network, whereasothers each focus on a specific advantage, e.g. [31] focuses ondesigning a low cost credit system where virtual tokens areeasily distributed and maintained; [30] focuses on designinga scheme where secure signatures are ensured to be checkedbefore forwarding; [36] focuses on the robustness and falsedetection of the reputation system. Some of the above schemesuse centralized authority to maintain the reputations/credits,and some propose fully distributed schemes.

Designing incentives for wireless networks with networkcoding is very different from the ones for conventional for-warding for two major reasons. First, games and incentives forforwarding have a predefined target action, i.e. nodes shouldforward instead of dropping under any condition. When theNC option is also considered, the utility of NC depends onnetwork conditions (e.g., packet loss rate), so there is no apriory defined target action. In particular, when the networkcondition is not good but also not extremely bad, the nodes areincentivized to perform NC to improve the delivery rate. Whenthe network condition is either perfect or very bad, NC is notneeded or cannot help, respectively. Thus, nodes should notbe incentivized to perform NC. In section V, numerical resultson how the sustainability varies over the packet loss rate ispresented, shown in Fig. 5. Another important difference isthat adding more actions, i.e., adding the NC option in additionto forwarding or dropping, further increases the complexity.This leads to additional challenges in the design of the socialstrategy and reputation update rules. However so far very littlework has been done to design incentives for networks with NC.The only schemes we know are a credit scheme [37] and areputation scheme [38].



Comparing between the two major types of incentiveschemes, reputation schemes are advantageous over credit ortoken schemes in the following aspects: first, the tokens arevery difficult to implement. If tokens are simply cryptographicpackets, they can be easily duplicated and cannot be usedas currency. So the implementation of tokens needs specialhardware imbedded techniques. Second, the transactions oftoken before each transmission introduce a large overheadand serious delay. Due to the the above reasons, we deployreputation schemes instead of tokens.

The existing reputation scheme for network coding in wire-less network [38] is far from complete due to the followinglimitations: first, the existing work does not have rigorous for-malism for NC forwarding using games. Second, the incentivecompatibility constraints are not considered in the existingwork, i.e., the conditions under which the incentive scheme canbe complied by selfish users, which is essential and importantfor any incentive design. Third, the reputation update rule isnot optimized. Fourth, the existing work proposed a centralizedreputation management scheme with the help of a centralauthority for wireless mesh network, however such schemeis not feasible for pure MANETs in most cases.

Our incentive scheme is also based on reputation, however,is significantly different from the previous one in these aspects:

• for the first time it models the (secure) network codingand forwarding in wireless networks as an infinite anddiscounted repeated game and provides rigorous gametheory formalism.

• it provides a set of social norm based reputation schemeswhich are specifically designed for mobile networks withselfish users to encourage network coding.

• it formalizes the social norm selection as an optimizationproblem with incentive compatible (sustainability) con-straints, and solves the problem with both theoretic andnumerical analysis.

• it analyzes the impacts of network parameters to ourscheme including packet loss rate, the costs of forwardingand coding, and the stability of the network (persistencefactor).

• it discusses some practical issues including the imple-mentation details and costs of the distributed reputationscheme, transmission sessions with multiple hops, theexistence of malicious and altruistic nodes in the network.

III. SYSTEM MODEL

A. Network Model and Network Coding Scenario

We consider a wireless ad hoc network, where mobiledevices can act as source, sink or relay nodes at different timesor simultaneously in different sessions, as shown in Fig.1.

Intra-flow network coding is used to increase transmissionreliability on lossy wireless channels. The source generatesa stream that is segmented generation by generation, wheregeneration size = K packets. The source then injects inthe network K packets that are linear network coded, i.e.,a linear random combination of the initial generation packets.Redundancy is required to overcome losses on link (R,D) witha packet loss rate denoted as p. When an intermediate node R

Fig. 1. The same node N acts as a relay node in session 1 and 2, a sourcenode in session 3 and a sink node in session 4.

receives K encoded packets from its predecessor node (in ourcase, source node S), it generates and forwards to the nexthop (i.e., sink node D) n random linear coded packets[3]. Theratio n/K (where n >= K) is defined as redundancy rate. If asecure NC scheme such as homomorphic signature is used toprotect packets from pollutions, the procedure is no differentfrom regular random linear network coding except for the extraprocessing overhead.

The probability of delivering K packets with n transmis-sions on a faulty link follows a negative binomial distributionwith parameter 1−p. So the expected number of transmissionsE(n) is K/(1−p), which means the redundancy rate should beset to 1/(1−p) to achieve full delivery. If less than K linearlyindependent packets are received, the entire generation is lostbecause the receiver cannot decode. “Progressive coding” isused here to overcome this problem, where the intermediatenode forwards the full generation without coding but onlyencodes the redundant packets. The advantage of progressivecoding is a lower decoding delay and also the ability toreceive some packets at the destination even if the full rankis never received. This scheme is clearly attractive if someof the intermediate nodes in the path are not capable tocode. In particular, if the non coding node is in the criticalsection, the destination receives all (and only) the packets inthe generation that survive link loss along the path.

To simplify the model, without loss of generality, we assumethat the intermediate node knows a priori loss rate p andintroduces redundancy accordingly, i.e., it injects K/(1 − p)packets, of which K are the original packets and the rest arecoded packets.

The nodes in our model are mobiles with the followingcharacteristics: having limited power resources, followingselfish algorithms and being randomly matched as sessionorigin, relay and destination. Here selfishness means takingan action to maximize its own utility. The possible action ofan intermediate node includes performing NC, simple forward-ing or dropping the packets totally. Relatively high mobilityforces the devices to have different neighbors throughout time.Hence, we use a global distributed reputation system (say,reputation reports are signed and periodically broadcast to ascoped neighborhood) to keep track of the reputation value ofeach node. This way, each node has a consistent view of thereputations of the other nodes. More detailed discussion onsuch distributed reputation maintenance system is presentedin Section VII.

The model described above is rather simple (unicast sessionon a single path), yet it captures the worst damage a node R



TABLE II

THE UTILITY MATRIX OF ONE-SHOT NC FORWARDING GAME

can cause by being not cooperative. In the more general case,a MANET with multiple paths is deployed from S to D. In thiscase the non-cooperation of a node has a less severe effect thanin the single path case because of path redundancy. The singlepath model reflects the worst-case situation over all possibletopologies and routing schemes. In section VII.B, we discussthe extension to multi-hop, multi-path and multicast scenarios.We also summarized the limitations of the current model andtheir potential improvements in the future work (section VIII).

B. Game Setting

We model the unicast session in part A as a one-shot NCforwarding game G = (N ,A, u). N is the set of players inthis game. There are two players: player 1 is the intermediatenode R and player 2 is the source-destination (S-D) pair ofthe session. So N = {R, S-D}. A = (AR, AS-D) is the set ofactions for each player. Intermediate node R, has three actions:(1) NC-forward (NCF) K/(1 − p) encoded packets to sinknode D; (2) simply forward (F) the original K packets to D;(3) totally drop (Drop) the packets. So AR = {NCF, F, Drop}.The source-destination pair, has no actions, so AS-D = ∅. Theutilities of each player when an action is taken are shown inTable.II. We assume the S-D pair receives a constant benefitof B for each delivered packet. The intermediate node R hasa constant cost of c1 for encoding each packet, and a constantcost of c2 for forwarding each packet. Here c1 and c2 mainlyrepresent the power consumption of coding and forwarding.

As system designers, we encourage nodes to perform NCFif and only if the overall utility of performing network codingis larger than simple forwarding; and obviously the utility ofperforming simple forwarding should be larger than dropping(which is 0). So the game itself must satisfy the condition inequ.(1).

B − (c1 + c2)K

1 − p> B(1 − p) − c2 > 0 (1)

Nodes in the network are assumed to be selfish strategicplayers who take the action to maximize their own utilities. If itis a one-shot game, there is a dominant action (or best choice)for intermediate node R, i.e., total drop (Drop). Therefore thenetwork has zero throughput. Besides, one-shot game is notappropriate to model nodes that stay in the network for arelatively long time. So we model it as an infinitely repeatedgame with persistence factor δ. δ represents the probability ofplaying the game once again in the future. Namely, it reflectsthe likelihood that a node will stay in the system for thenext time period. While some nodes are leaving the network,some new coming nodes arrive, forming a dynamic balanceof the population. δ is decided by the nodes themselves andis not tunable by system designers. Having a low average δindicates that nodes join and leave the network frequently.

δ = 1 indicates that all existing nodes stay in the networkwhereas no new nodes come. We will first assume δ is constantand given when selecting the optimal social norm. Later wewill discuss how different δ affects our design.

As mentioned in the previous section, a relay node inone session may be a source/sink node in another session,and a current relay node will probably become a source/sinknode in the future. We assume three nodes in the session arerandomly matched and every node has the same chance ofbeing a source, relay or sink node. So expectedly, in everythree sessions, a certain node in the network will act as relay,source and sink respectively. Namely, we assume the nodesin the network are uniform, i.e., having the same chance ofmatching and sharing the same parameters of δ, B, c1, c2, p, K ,etc. Expectedly, in every three sessions, a certain node in thenetwork will act as relay, source and sink respectively. Thelong-term utility of a node is:

u∞ =∞∑

t=1

δt−1(utR + ut

SD) (2)

If every node has fixed neighbors and plays the repeatedgame with the same opponents over time, simply adoptinga tit-for-tat strategy will be enough to enforce the nodes toperform network coding. However, mobiles usually changeneighbors throughout the experiment, so they do not haveknowledge of their new neighbor’s behavior history. Undersuch circumstance, tagging each node with a reputation valueis efficient to record its behavior in the past. By introducing theidea of social norm from economics to wireless networks, wedesign a novel incentive scheme to encourage nodes to performnetwork coding despite of the expensive power consumption.

C. Social Norm

The social norm, denoted by κ, is composed of a socialstrategy σ and a reputation scheme τ .

In our reputation system, every node in the network istagged with a reputation θ. Reputations are updated period-ically, so θ is a constant within each period. We consider thecase where reputations take values from a finite set. Withoutloss of generality, we assume that θ is an integer from thefinite set Θ = {0, 1, . . . , L} for some L. A high θ means thatthe node performed well (e.g. coding and/or forwarding) inhistory, otherwise the node did not perform well in the past.

The reputation system has the following structure: (1) everynode maintains a table that stores all its neighbors’ reputationvalues; (2) nodes broadcast deviating reports to a scopedneighborhood periodically (3) each node updates the repu-tations of its neighbors according to the deviating reportsreceived within the period.

σ is a reputation-based behavioral strategy, which is repre-sented by a mapping σ : Θ × Θ2 → A, where the first Θ isthe reputation of the intermediate node R, and Θ2 representsthe reputations of the S-D pair. A = {NCF, F, Drop}. So σspecifies the action σ(θR, θS , θD) ∈ A which node R withreputation θR should select when faced with a unicast sessionconsisting of a source node with reputation θS and a sink nodewith reputation θD.



Generally, the social strategy rewards high reputation nodes,or highly cooperative nodes, by prescribing intermediate nodesto perform coding and forwarding for them; also, it punisheslow reputation nodes, or deviating nodes, by prescribing inter-mediate nodes to drop their packets. We restrict our attentionto a set of threshold-based strategies Γ. Every strategy σ ∈ Γcan be characterized by a threshold k(σ) ∈ {0, 1, . . . , L}.Since there are at least three nodes in session (S,D,R), andso three reputations, there are many possible alternative socialstrategies. The social strategies in (3)(4) are two examples.Among all possible strategies, σ2 is the strictest (i.e., nodeR performs NCF only if both source and sink nodes havereputations higher than L). In this paper, we mainly use σ1

as our proposed social strategy (here R performs NCF if atleast one of the source and sink has higher reputation than L).The reputation update in our scheme lowers the relay node’sreputation only when misbehavior (i.e. performing a worseaction than the prescribed action) is detected, whereas per-forming F/NCF when the prescribed action is “drop” does notcount for such misbehavior. So prescribing “drop” when therelay node’s reputation is low simply allows low reputationnodes to automatically recover their reputation without extraefforts. This strategy is only one among many valid strategies;however, various strategies result in different performancesunder different network conditions ï¿½ there is no optimalstrategy for all network settings and set-ups. We will alsocompare σ1 with other alternatives and analyze the impactsof choosing different strategies in part A of SectionIV.

σ1(θR, θS , θD) =

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

NCF if θR = L& max{θS, θD} = L

& min{θS , θD} ≥ k

Drop if min{θR, θS , θD} < k

F Otherwise

(3)

σ2(θR, θS , θD) =

⎧⎪⎨

⎪⎩

NCF if θR = L& min{θS, θD} = L

Drop if min{θR, θS , θD} < k

F Otherwise

(4)

Consistent with our threshold-based social strategy σ1,we propose a “multi-stage punishment reputation scheme”denoted as τ , expressed in formula (5), where x denotes thenode’s behavior. Generally, if an intermediate node alwayscomplies with strategy σ1, represented as x = 1, its reputationwill increase by 1 until it reaches the maximum L; if it deviatesfrom σ1 for at least once within the period, its reputation willdecrease to either k or 0, depending on its deviating action—if it drops packet totally when it should not (i.e. x = 2), itsreputation will decrease to 0; otherwise, only decreases to k(i.e. x = 1). The “multi-stage punishment reputation schemeis shown in Fig.2, where α′

1, α′2 are transition probabilities

caused by approved behavior and ε′11, ε′12, ε

′21, ε

′22 are transi-

tion probabilities caused by evil behavior.

τ(θ, x) =

⎧⎪⎨

⎪⎩

min{L, θ + 1} x = 0k x = 10 x = 2.

(5)

Fig. 2. Multi-stage punishment reputation scheme τ .

IV. GAME OPTIMIZATION

A. Metrics

We design social norm based incentives to encourage nodesin the network to cooperate, aiming at maximizing the trans-mission performance (packet delivery rate) of the network. Weuse the total number of packets delivered in all sessions in thenetwork within one time period as the metric of transmissionperformance. Taking the costs (the power consumptions) intoaccount, we use social utility as a metric of the system. Socialutility is defined to be the total utility of all nodes in thenetwork after one time period.

Another important metric for an incentive scheme is theobedience of the nodes, i.e., sustainability of the social norm.A social norm will be sustained, i.e., can persist for everleading to a stable solution, when selfish nodes choose tocomply with the social strategy σ instead of deviating fromit. In our case sustainability is guaranteed when the properpunishment is enforced, namely when an intermediate nodewill have a long-term utility decrease if it does not performcoding and/or forwarding when it is prescribed to do so.Sustainability reflects the probability that a selfish node willchoose to cooperate and help others. The more intermediatenodes perform coding, the higher delivery rate the networkwill achieve; so the sustainability of the incentive scheme alsoaffects the transmission performance.

System designers have to consider both aspects, i.e., socialutility and sustainability, when selecting parameters of thesocial norm based protocol. We wish to maximize bothaspects, however we note that very often there is a tradeoffbetween the two aspects.

B. System Convergence

Given the social norm represented by social strategy σ1

in (3) and reputation scheme τ in (5), we derive the stationarydistribution of reputation in this subsection. Initially everynode is assigned with the maximum reputation value L. Afterinteracting with other nodes for some time, the distribution ofreputation will converge to a fixed distribution η(θ).



We assume that each node engages in M sessions acting asa relay node within one time period. We use m1 and m2 todenote the number of NC and F sessions for a high reputationintermediate node (an intermediate node with θR = L). We usel to denote the number of F sessions for a medium reputationintermediate node (an intermediate node with θR ∈ [k, L)).The reputation update probabilities shown in Fig.2, includingα′

1, α′2, ε

′11, ε

′12, ε

′21, ε

′22, are all functions of {packet loss rate

p, packet delivery rate q(= 1−p), NC generation size K , m1,m2, l}. Specific definitions are in Appendix.

Proposition 1: When all nodes follow the previouslydefined social norm, the reputation distribution of nodes inthe network converges to a unique point {η(θ)} in (6).

η(L)−1 =(1 + ε′21 + ε′22 − kε′21)(1 − α′

1)(1 − α′L−k2 )

(1 − α′2)α

′L−k2

+ (k + 1)(

1 − α′1

α′L−k2

− ε′11

)+ 1 + ε′12

η(θ) =1 − α′

1

α′L−θ2

η(L), if k ≤ θ ≤ L − 1

η(θ) =1 − α′

1

α′L−k2

η(L) − η(0), if 1 ≤ θ ≤ k − 1

η(0) = ε′11μ1 + ε′21μ2

μ1 = η(L)

μ2 =L−1∑

θ=k

η(θ) =(1 − α′

1)(1 − α′L−k2 )

(1 − α′2)α

′L−k2

η(L) (6)

Where μ1, μ2 and μ3 = 1 − μ1 − μ2 are respectively theproportions of nodes with a high, medium and low reputationat the steady state, as illustrated in Fig.2. Since we assume thatthe nodes in a unicast session are randomly matched, then eachnode has a probability of μ1 to have θ = L, a probability of μ2

to have k ≤ θ < L and a probability of μ3 to have θ < k.In typical non pathologic situations, μ3 is very close to zero.

C. Social Utility at Steady State

In this subsection we determine the social utility (total utilityof all nodes in the network) at steady state for social norm κwith reputation distribution η(θ) in (6). According to thesocial strategy σ1, a session containing low reputation nodes(either S, D or R) always has a utility of 0, because lowreputation nodes always drop others’ packets and their ownpackets are also dropped by others as punishment. So weonly consider the sessions where all nodes have reputationsθ ≥ k. As defined in part B, m1 and m2 are the numbers ofNC and F sessions with a high reputation intermediate nodein one period; l is the number of F sessions for a mediumreputation intermediate node in one period. Since all nodesare considered uniform, the expected utility of any node inthe network per one-hop session is:

U =∑

θ

η(θ)v(θ)

=13μ1 ×

[m1

M(B − c1 + c2

q) +

m2

M(Bq − c2)

]

+13μ2 ×

[l

M(Bq − c2)

](7)

Where

m1 = M(μ2

1 + 2μ1μ2

)

m2 = Mμ22

l = M (μ1 + μ2)2 (8)

We now extend the results to a multi-hop sessionwith H hops, i.e., H intermediate nodes, expectedly thereare μ1H high reputation intermediate node which can performNCF, and μ2H medium reputation intermediate node whichcan only do F. In practice, the fraction of nodes with lowreputation, i.e., μ3, is very close to 0. In other words, we cantake an approximation as μ1 +μ2 = 1. So the expected utilityof a session with H hops is approximately:

UH =m1

M

(Bqμ1H − c2μ2H − c1 + c2

qμ1H

)

+m2

M

(BqH − c2H

). (9)

D. Sustainability Conditions

In this subsection, we determine the sustainability condi-tions, under which all nodes in the network will rationallychoose to comply with the social strategy σ1 instead ofdeviating from it. Based on the assumption that all nodes inthe network take the action to maximize their own long-termutility, we have the following lemma:

Lemma 1: When a social norm κ = (σ, τ) is applied, if thelong-term utility, shown in (2), of any node in the networkby complying with the social strategy is no smaller than thelong-term utility by deviating from the prescribed actions inthe social strategy, social norm κ is sustainable, i.e., for anyreputation θ ∈ Θ and any selfish strategy σ′ �= σ, we musthave:

v∞σ (θ) ≥ v∞σ′ (θ) (10)

where,

v∞(θ) = E

[ ∞∑

t=1

δt−1v(θt)

]

= v(θt=1) + δ∑

θ′pτ (θ′|θ)v∞(θ′) (11)

Initially, all nodes have θ = L. So we have μ1 = 1 andμ2 = μ3 = 0. According to (8), we have m1 = M andm2 = l = 0. Here l = 0 is because there is no mediumreputation node. In order to make sure all nodes comply withσ1 initially, all parameters must satisfy the conditions in (12)and (13). If (12) is satisfied, nodes will have a larger (or equal)long-term utility by performing NCF instead of F; if (13) issatisfied, nodes will have a larger (or equal) long-term utilityby performing NCF rather than Drop.(

B − c1 + c2

q

) ∞∑

t=1

δt−1 ≥ B − c2 + (Bq − c2)∞∑

t=2

δt−1

(12)(

B − c1 + c2

q

) ∞∑

t=1

δt−1 ≥ B − 0 + 0 ·∞∑

t=2

δt−1 = B (13)



Conclusion 1: If discount factor δ satisfies the conditionin (14), all nodes will perform NC as prescribed in σ1, andthe social norm will be sustained initially.

δ ≥ c1 + c2 − qc2

qB(1 − q)(14)

At any time after the initial point until the steady state,nodes will always comply with the social strategy iff. thelong-term utility will decrease if they deviate. By comparingthe long-term utilities of all possible deviations motivated byselfish intention, i.e., NCF → F, NCF → Drop and F → Drop,we obtain the sustainability conditions in (15)(16)(17).

δ

1 − δ

[B − Bq −

(μ1

μ2+ 2

)(c1 + c2

q− c2

)]

·μ1μ2 ≥ c1 + c2(1 − q)q

(15)

δ

1 − δ

[B

(1+

μ1

μ2

)+Bq

(μ2

μ1

)−

(2 +

μ1

μ2

)c1+c2

q− c2

μ2

μ1

]

·μ1μ2 ≥ c1 + c2

q(16)

δ

1 − δ

[μ1

μ2B + Bq

(μ2

μ1+ 2

)−

(μ1

μ2+ 2 +

μ2

μ1

)c2

]

·μ1μ2 ≥ c2 (17)

For steady state, all parameters must also satisfy the abovethree sustainability conditions.

(14)(15)(16)(17) can also be written as the form ofδ ≥ δ1, δ ≥ δ2, δ ≥ δ3, δ ≥ δ4 or δ ≥ max{δ1, δ2, δ3, δ4}. So,if max {δ1, δ2, δ3, δ4} < 1, the sustainability conditions canalways be satisfied if the actual δ of the nodes in the networkis close enough to 1, which indicates that the nodes will stayin the system forever. By computing inequalities (15)(16)(17),we obtain a threshold for B in (18), above which we havemax {δ1, δ2, δ3, δ4} < 1.

Proposition 2: If benefit B is large enough or at leastsatisfies:

B ≥ c1 + c2 − qc2

q(1 − q)

(μ1

μ2+ 2

)(18)

there always exists a δ ∈ [0, 1], s.t. when δ ≥ δ, the incentivescheme can be sustained by all nodes in the network. Here,

δ = max {δ1, δ2, δ3, δ4} (19)Since δ ∈ [0, 1] is decided by the nodes themselves and not

tunable, whether the social norm based incentive scheme canbe sustained is greatly decided by the system itself. So weuse the interval between δ and 1 as the metric to reflect thesustainability of the scheme.

Definition 2: The Sustainable Interval for an incentivescheme is defined as: SI = 1 − δ. In any game theoreticmodel based on discounted repeated games, SI can be used torepresent the sustainability of the incentive scheme. The largerSI, the more compliant and better performing the scheme is.

Nodes with discount factor δ falling in the interval(i.e., δ ≥ δ) will comply to the social strategy (do networkcoding/forwarding). A larger SI indicates that more nodes willcooperate and do network coding, so the network will achievea larger throughput.

E. Optimization Problem With Constraints

We formalize the parameter selection as an optimizationproblem with constraints, i.e., we aim at maximizing the socialutility U in (7) and (9) with the constraint of sustainabilitycondition, δ ≥ δ in (19), for any (μ1, μ2).

The parameters can be classified into two categories: onecategory reflects the nature of the network, and is fixed (nottunable by designers); the other reflects the characteristics ofthe social norm based scheme we propose, and can be tunedby the protocol designer.

In summary, fixed parameters include: packet loss rate p,benefit-cost ratio B : c1 : c2, discount factor δ, numberof hops H ; tunable parameters include: social strategy σ,reputation threshold k, number of sessions M within onereputation update period and NC generation size K .

V. PERFORMANCE EVALUATION - NUMERICAL ANALYSIS

In this section, we evaluate the performance of the NCforwarding game in the previously introduced scenario usingnumerical techniques. We compute social utility U and sus-tainability SI results as a function of system variables anddesign parameters. In particular we define the optimal selec-tion of reputation thresholds and other design parameters.Here, the evaluation is still under the assumption that nodesare randomly distributed and have equal chance to becomesource/relay/destination nodes in a session, as described insection III.A.

A. Selecting the Social Strategy σ

In part C of section II, we pointed out that there are manydesign choices for σ, and we presented two examples in (3)(4).In this subsection, we show that there exists a tradeoff betweensocial utility and sustainability when designing the socialstrategy. Specifically, a stricter social strategy (e.g. a strategythat requires high reputation of both source and destinationfor coding at the intermediate node) will lead to a highersustainability (i.e., higher compliance ratio) at the price ofa lower social utility. We discover this tradeoff by comparingthe social utility U and the sustainability interval SI of σ1

in (3) and σ2 in (4), where σ2 is stricter than σ1. In part (c)of Appendix, We prove that:

U1 ≥ U2 (20)

and

SI1 ≤ SI2 (21)

This happens because in σ2, the intermediate node performsnetwork coding only when all the nodes in the session havemaximum reputation of L. Naturally it harms the overallpacket delivery rate since it reduces the chance of coding.On the other hand, it enforces the nodes to be more compliantin order to keep a high reputation and avoid severe utilitydegradation.

B. Selecting the Design Parameters L, k and M

Fig.3 shows the numerical results of stationary social utili-ties U under different settings of threshold interval L− k andnumber of sessions in one reputation update period, M .



Fig. 3. Social utilities at steady states (U ) when selecting different thresholdintervals (L− k) and number of sessions M in one reputation update period.

In practice, when the social norm is applied, the selfishnodes are incentivized to behave well, so there are very fewnodes with reputation lower than k, since the probability thatall packets are unexpected lost is tiny. Hence the value of kalmost has no effect on network performance. Here we onlyconsider the setting of the interval between L and k. Accordingto Fig.3, U is high when L − k is set small. On the contrary,when L − k is set very large, U approaches the utility valuethat corresponds to all nodes only performing F. The intuitionis that if L − k is very large, medium reputation nodes haveto keep performing well for many periods of time in orderto reach L. During this long journey from k to L, they arestill medium reputation nodes which only perform (and areonly served with) F. Therefore the network has a lower overallpacket delivery rate. We also prove mathematically that U isa strictly decreasing function of L − k in Appendix.

Fig.3 also shows that U increases when M gets smaller.It means that if the system updates or refreshes reputationsfrequently, i.e., there are fewer sessions in an update period,the network will have a better packet delivery rate. Intuitively,if refreshing rate is higher, the nodes’ reputations more accu-rately reflect their behavior history. And they will be rewardedor punished in time. We also prove mathematically that U isa strictly decreasing function of M in Appendix.

Fig.4 shows the numerical results of sustainable interval (SI)under different settings of L − k and M .

According to Fig.4, SI is generally higher when L− k andM are set smaller. When L − k and M are set very large,SI approaches 0, i.e., nodes will not comply with the socialstrategy σ1. The reason is similar to U , i.e., if L−k and M arelarge, a medium reputation node will take too long to becomea high reputation node, and it probably will leave the systembefore its reputation reaches L. Considering its own long-termutility, it naturally has less incentives to perform well.

C. Impact of Non Configurable System Variables(p, B : c1 : c2, δ) on Performance

In the above subsections, we did not discuss the setting ofNC generation size K . According to numerical tests, changingK has little impact on system performance. Intuitively, for

Fig. 4. Sustainable interval (SI) when selecting different threshold intervals(L − k) and number of sessions M in one reputation update period.

Fig. 5. Sustainable interval (SI) of the incentive scheme under differentpacket delivery rate q.

both NCF and F, we mainly care about the proportion of pack-ets delivered, so the value of K does not affect results. Thisis verified by the simulation result shown in Section VII.B.

In part D of section III, we have thoroughly discussed theimpacts of discount factor δ (i.e., the probability of a nodestaying in the system for the next period) on the sustainabilityof our scheme. The higher δ, the more sustainable the systemis. There exists a threshold of δ, i.e., δ, below which nodeswill not comply or perform network coding, above which theywill. This indicates that a node that will stay in the system fora long time is more likely to help others than the node thatwill leave the system soon.

Also in part D of section III, we show that there exists a B,below which the scheme can never be sustained. Benefit Bis a relative parameter evaluated by each node itself. If anintermediate node highly values the benefit of its own futuretransmissions, it has more incentives to serve others and pursuea high reputation. If δ is low, a high B is still insufficientto encourage nodes to do network coding, hence the packetdelivery performance does not increase.

A low packet loss rate p, or a high packet delivery rate q,will lead to a higher throughput and social utility, which isobvious. Fig.5 shows how the sustainability of the schemevaries as a function of packet delivery rate. When the packetloss rate is very low, the network condition is good, andnobody does expensive secure NC because the transmission



Fig. 6. Overall packet delivery rate under different wireless link loss rate.

result of doing NC is hardly different from doing F. When thepacket loss rate is very high, the network condition is very bad,and nobody does expensive secure NC either, because even ifthey do NC, nobody notices and they will be punished anywaydue to the severe packet loss. In realistic scenarios, the packetloss rate is generally well below 0.5. With this condition, wemay conclude that our incentive scheme is more sustainable(i.e., more nodes are induced to use Network Coding) whenpacket loss increases, just as NC is beneficial when packetloss is serious.

VI. PERFORMANCE EVALUATION - SIMULATIONS

We extended our work by performing simulations on amobile ad hoc network consisting of 30 nodes that are ran-domly located within 1 km2 area and slowly moving towardsrandom directions over time. Each node starts a unicasttransmission session at a random time within 60s and lastsfor a random period of time. The maximum reputation is setas L = 10 and the reputation threshold k = 6.

A. Packet Delivery Rate

Fig. 6 shows the simulation results of overall packet deliveryrate under different wireless link loss rate. Here we set NCgeneration size K = 32. The red line shows the performanceof the scenario where all the relay nodes only perform for-warding - it is intuitive that the overall packet delivery rate isclose to (1−p), where p indicates the link loss rate. The blueline shows the performance of the scenario where the socialnorm is applied - it significant slows down the performancedegradation caused by increased wireless losses.

B. NC Generation Size

To learn the impact of NC generation size to the transmis-sion performance in our scheme, we vary the generation sizein the simulation, and examine its impact on the delivery rate.Fig. 7 shows the overall packet delivery rate under differentNC generation size. Here link loss rate p = 0.3. We see thatthe generation size does not show a clear positive or negativeimpact on the delivery rate. As discussed in section III.A,in this paper, we use “progressive coding”, where only theredundant packets are encoded. In this way, we can avoid

Fig. 7. Overall packet delivery rate under different NC generation size K .

the total generation loss caused by not receiving enoughindependent NC packets. Progressive coding should be themajor reason why generation size does not significantly affectpacket delivery rate or social utility.

VII. PRACTICAL ISSUES

In this section, we consider some practical issues of apply-ing the social norm based protocol to mobile ad hoc networks.

A. Distributed Reputation System

As mentioned before, centralized or partially centralizedreputation management with a reputation administrator ormultiple reputation managers is not feasible for wireless ad hocnetworks. We adopt a fully distributed reputation managementsystem where nodes disseminate reputation information toscoped neighbors of limited hops periodically. Research hasbeen done to minimize the cost of reputation data dissem-ination by encoding the reputation packets[21], as well asto recognize and prevent fake reputation reports[36]. We tryto optimize the reputation system by solving the followingthree major problems: (1) what’s the simplest message formatto broadcast and update reputation information; (2) what’sthe best reputation update frequency if taking the cost ofreputation dissemination into account; (3) to what scope ofneighbors do nodes disseminate the reputation information.

According to the reputation update rule τ explained inpart C of section III, a node’s new reputation is decided byits old reputation and its behavior in the last period. Initiallynodes have the uniform reputation information: all nodes aretagged with initial reputation θ0. If all nodes in the networkhave consistent reputation information at the beginning ofperiod i, as long as they receive consistent information aboutthe behavior of others in period i, and calculate the newreputations according to τ at the end of period i, then theywill have consistent updated reputation information at thebeginning of period i + 1. Hence, disseminating reputationvalues and distinguishing the updated info from out-of-dateinfo is not necessary and should be replaced by disseminatingnodes’ behavior instead. So problem (1) is reduced to: in whatformat do nodes broadcast the behavior of their neighbors.

Since reputations are updated only at the end of each period,nodes only need to broadcast a single message, which is



TABLE III

REPUTATION UPDATE MESSAGE FROM NODE i

a summary of its neighbors’ behaviors during the period.There are two possible types of deviating actions: performDrop when it should have performed F or NCF (case 0) andperform F when it should have performed NCF (case 1). Thedeviating node’s reputation should be decreased to 0 for case 0and decreased to k for case 1. Let x denote deviating actions.If a node has j deviating actions within one period, the worstbehavior is considered, i.e., x = x1 ∩ x2 ∩ . . . ∩ xj . So thedeviating action can be represented as a one-bit message:0 indicating reputation down to 0 and 1 indicating downto k. If Node i has ni deviating neighbors and their NodeIDs are {di0, di1, . . . , di,ni−1}, its reputation update messageshould be in the format shown in Table.III. For a networkgraph G(N , E) with maximum degree k̄(G), if it has no morethan 256 nodes (|N | ≤ 256), then the size of node ID is1 byte, and the largest message has size of 9 ∗ k̄(G) bits.Even if G is one big cluster (i.e., k(G) ≡ |N | − 1), whichis not quite possible for ad hoc networks but is the worst-case with the most information redundancy, the message sizeis approximately 1/4 of a regular packet size. The reputationinformation can also be combined as a header of regular videopackets when the message size is very small.

If the nodes are static, i.e., every node has fixed neighbors,then it would be sufficient to broadcast reputation updatemessages within 2 hops. If the network structure and neighborsare changing all the time, broadcasting to farther neighborhoodis necessary. Although the scope of reputation broadcastinggreatly depends on the mobility of the nodes, however nodescan always broadcast queries and retrieve reputation informa-tion from others upon need, and neighbors are relatively fixedwithin each period due to high reputation update frequency.So, in order to save cost of message dissemination, thereputation message broadcasting can be restricted to 2 hops.

As concluded in part C of section IV, the more frequentlyreputations are updated, the better system performance can beachieved. However, updating reputation more frequently leadsto higher message dissemination costs as well. Let c3 denotesthe cost of broadcasting one reputation update message to two-hop neighbors. If the ratio between the sizes of a reputationupdate message and a regular packet is f (0 < f < 1), thenc3 ≤ (k(G) + 1) ∗ f ∗ c2. The cost is estimated to be fairlyinsignificant comparing to regular packets. Even when M = 1,i.e., one update for each generation transmission, it would notflood the network. Besides, many routing protocols, such asOLSR, have routing information updates periodically. Hence,the reputation information can be attached to the routinginformation updates.

B. Extension to Multi-Hop, Multi-Pathand Multicast Scenarios

For multi-hop scenario, as the number of hops H in asession increases, the chance of packet loss increases, thereforethe social utility UH and the throughput decrease. In a typical

Fig. 8. Social utilities at the steady state when the number of hops H in asession varies.

stable MAENT, the number of hops needed to reach any nodein the network should not be very large, and when the numberof hops is small, there is limited degradation of performance.When the number of hops is less than 4, the utility is stillbetter than the case where no network coding is applied. Onthe other hand, H does not affect the sustainability of theincentive scheme, nor the parameter selections, because eachintermediate node within a session makes forwarding decisionsindependently, based on the knowledge of the reputation valuesof itself, the source and the sink node only. Fig.8 shows thatthe social utility decreases if the number of hops (or numberof intermediate nodes) in the session increases. Here UH

κ isan approximate value where we assume every node in thesession at least does F and nobody totally drops the packets,because there are a tiny fraction of nodes with reputationslower than k. That is also why the value of k does not affectsystem performance. When H = 1, UH � U , which in turntestifies our equations in (7) and (9).

In multi-path scenario there exist redundant paths. However,the intermediate nodes along the redundant paths still followthe same social strategy. Hence multi-path scenario is equiva-lent to multiple unicast sessions over the same pair of sourceand destination nodes.

In the multicast case, the destinations submit their requeststo the source thus forming a multicast tree. The internal treenodes prune the leaves with low reputation until the reducedtree has only high/medium reputation leaves. The source thenmulticasts the file over the branches of the tree as shown inFig.9. Each down stream node reports the misbehavior of theupstream node according to its action (NCF, F or Drop). Thecareful reader will notice that some internal tree nodes orleaf node that can overhear will get the NCF delivery eventhough they have low reputations, thus, they get a “free ride”.A possible solution is for each source to issue periodically asymmetric crypto key to high reputation nodes, and to use thatkey to distribute the file on the multicast tree. In this case, lowreputation nodes that serve as relays are properly penalized asthey cannot read the encrypted file. Yet they can still performnetwork coding and thus improve their reputations. There isclearly a trade off between the benefit of complete enforcementof the rule (i.e., elimination of free rides) and the performance



Fig. 9. Multicast scenario. Here D2 and D4 have low reputations; othernodes have high reputations.

cost of distributing the crypto key to qualified receivers. Theevaluation of this tradeoff will imply the detailed design of anefficient key distribution strategy. It is beyond the scope of thiswork and is left for future study. Besides, such “free ride” willnot affect the sustainability of the social norm because the freeride is granted randomly, it is not expected nor guaranteed.Nodes with low reputation still expect punishment in mostcases, so the social norm still incentive works.

C. Networks With Altruistic, Maliciousand Intermittent Nodes

So far we assumes that all the nodes are selfish and rational,i.e., choose the action that maximizes its own utility. Usuallysuch users are called “reciprocative” users. Now we considerthe following cases where some users are:

• altruistic, i.e., always perform NC and forward;• malicious, i.e., drop packets intentionally and upload

bogus packets.Altruistic users themselves do not need to be incentivized,

however the existence of altruistic users will encourage selfishbehavior of other selfish nodes — some selfish behavior is notpunished. Our social strategy prescribes that a relay shouldtake actions corresponding to the reputation of source anddestination nodes. In this sense, the altruistic users deviatefrom the prescribed strategy — they are supposed to drop thepackets from low reputation nodes, but they choose to networkcode / forward the packets. In order to avoid the negativeimpacts of altruistic nodes, a modification for the reputationupdate rule should be enough, i.e., include the improperaltruistic behavior as a type of deviating action, and punishthe altruistic nodes by reducing their reputation.

Malicious nodes that intentionally drop packets will receivelow reputation immediately according to our current reputationscheme. So neighbors will refuse to forward the packets com-ing from malicious nodes, which effectively stops the spreadof bogus/spam information. Hence, our incentive scheme hasa by-product of protecting the network from malicious attacks.

VIII. CONCLUSION AND FUTURE WORK

In this paper, we present a social norm based incentivescheme for mobile ad hoc networks, where nodes are selfish,

strategic users. For simplicity, we consider a single-pathunicast session, where the intermediate node can rationallychoose to do secure network coding and forward packets withredundancy (NCF), simply forward the original packets (F) ortotally drop the packets (Drop). We model the unicast sessionas a repeated gift-giving game with persistence factor δ, wherenodes are symmetric and randomly matched. Our incentivescheme consists of a social strategy σ and a reputationscheme τ , which reward cooperative nodes by increasingtheir reputation and promising better transmission quality inthe future, and punish uncooperative nodes by decreasingtheir reputations and refusing coding/forwarding their packetsin the future. Most existing incentive schemes only propose asingle protocol and prove it can incentivize nodes to performcoding/forwarding. Differently from previous schemes, wepropose a set of social norm based incentive schemes withparameters that we adjust to optimize the social utility andsustainability. We first prove that the reputation distributionwill converge to a unique steady state, corresponding to a fixedsetting of the parameters. Then we present a series of resultsfor parameter selection that are supported by mathematicalderivations and numerical analysis: (1) there exists a tradeoffbetween the social utility and sustainability — a stricter socialstrategy will increase the sustainability but decrease the utility;(2) both utility and sustainability will be optimized if thereputation threshold k is set close to the maximum reputationL, and reputations are updated or refreshed frequently;(3) NC generation size does not affect the performance ofour incentive scheme, which is also verified by the simulationresult. We extend our work with simulations and show thatour social norm significantly improves the network’s overallpacket delivery rate over the scenario where nodes onlyperform forwarding. Additionally we show how the networkcondition or the game itself impacts our incentive scheme.Moreover, practical issues for the proposed reputation systemare discussed, including the distributed reputation system, aswell as the existence of altruistic and malicious users.

The following summarizes a few limitations of our currentscheme and directions for future work.

First, our design did not consider the costs associated withimplementing pollution protection mechanisms for networkcoding such as homomorphic signatures or file reassemblyand mixing with new signatures at intermediate nodes [6]. Wenote that different pollution protection schemes have differentbenefits, performance costs and limitations. They affect thedesign social norm design in different ways. Because of thesereasons we have opted to present a general social norm frame-work. This general framework can be easily customized to thevarious deployment scenarios and their specific characteristics.Future work will consider the impact of specific pollutionprotection mechanisms and their associated costs and benefitson social norm design and performance.

Second, the social norm reputation scheme is vulnerable toattacks such as faking reputation and collusion, just like anyreputation-based system is. Since this paper deals with theproblem of selfish nodes that are reluctant to perform networkcoding because of the costs, and with the design of incentivesto encourage them to comply, we focus on the effectiveness of



TABLE IV

NOTATION LIST

different incentive strategies and reputation schemes under theassumption that there are no malicious users. The protection ofthe reputation system from malicious users is a known problemfor which solutions exist, such as [44] [45], and can be appliedto our case. Thus, it is recognized as an important problem tobe solved before implementation, but it is deferred to a futurestudy.

Third, as discussed in section VII.B, in multicast scenario,sometimes low reputation nodes are not punished becausethey are relay nodes at the same time, or they can overhearthe transmission of a nearby high/medium reputation nodes.Although such imperfect enforcement does not affect the sus-tainability of the social norm or effectiveness in encouragingselfish nodes to behave well, it can be corrected in future work.

APPENDIX A

see notation list in Table IV.

APPENDIX BPROOF OF PROPOSITION 1

μ1 =αL−k

2

1 − α1η(k) +

1 − δ

1 − α1(22)

μ2 =1 − αL−k

2

1 − α2η(k)

μ3 = 1 − μ1 − μ2

At the steady state, we have ηt(θ) = ηt+1(θ) = η(θ) forany θ ∈ [0, L]. By computing the set of equations, we obtainthe stationary distribution in (6). Since we assume that thenodes in a unicast session are randomly matched, then eachnode has a probability of μ1 to have θ = L, a probability of μ2

to have k ≤ θ < L and a probability of μ3 to have θ < k.In typical non pathologic situations, μ3 is very close to zero.

APPENDIX CPROOF OF EQUATION (20) AND (21)

The social utility U of any σ is shown in (7). Parametersm1, m2, l corresponding to σ1 are shown in (8). m′

1, m′2, l

′

corresponding to σ2 are as follows:

m′1 = Mμ2

1

m′2 = M(2μ1μ2 + μ2

2)l′ = M(μ1 + μ2)2 (23)

Based on (1) (i.e., (B − c1+c2q ) ≥ (Bq − c2)), we have:

U1 − U2 = 2μ1μ2

[(B − c1 + c2

q) − (Bq − c2)

]× 1

3μ1 ≥ 0

So we prove that U1 ≥ U2.According to σ2, the long-term utility in (2) and the

sustainability condition in (10), in order to make sure thatthe nodes will have long-term utility decrease if they deviate,we must have:

μ21(B − Bq − c1 + c2

q+ c2)

δ

1 − δ≥ c1 + c2(1 − q)

q

Comparing with the sustainability conditions for σ1 in (15),we have δ1 ≥ δ2 unless μ1 � μ2, which will not happen aslong as we choose L − k and M properly. So we prove thatSI1 ≤ SI2.

APPENDIX DPROOF OF MONOTONY

According to the stationary distribution of reputation {η(θ)}in (6), we have:

μ1

μ2=

(1 − α′2)α

′L−k2

(1 − α′1)(1 − α′L−k

2 ).

Where α′1, α

′2 ∈ [0, 1] decrease when M increases. It is

easy to find out that μ1μ2

decreases monotonically withL − k and M . According to the definition of social utility,U increases monotonically with μ1

μ2(a better throughput when

a larger fraction of nodes do network coding). So U decreasesmonotonically with L − k and M .

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Chuchu Wu received the B.S. degree from the Electrical Engineering andInformation Science Department, University of Science and Technology ofChina, in 2010, and the Ph.D. degree from the Computer Science Department,University of California at Los Angeles, Los Angeles, CA, USA, in 2015. Sheis currently a Research and Development Software Engineer with TeradataCorporation, Los Angeles. Her research interests include network systemmodeling and optimization, wireless ad hoc networks, and big data.

Mario Gerla (M’75–SM’01–F’03) received the B.E. degree from the Poly-technic University of Milan, Italy, and the Ph.D. degree from Universityof California at Los Angeles (UCLA), Los Angeles, CA, USA. At UCLA,he was a part of the team that developed the early ARPANET protocolsunder the guidance of Prof. L. Kleinrock. At Network Analysis Corporation,NY, USA, from 1973 to 1976, he helped transfer ARPANET technologyto government and commercial networks. He is currently a Professor incomputer science with UCLA. He joined the UCLA faculty in 1976. AtUCLA, he has designed and implemented network protocols, including ad hocwireless clustering, multicast (ODMRP and CodeCast), and Internet transport(TCP Westwood). He has led the $12 million, six-year ONR MINUTEMANProject, designing the next-generation scalable airborne Internet for tacticaland homeland defense scenarios. His current research projects cover the designand performance evaluation of protocols and control schemes for ad hocwireless networks, and routing, congestion control, and bandwidth allocationin wide area networks.

Mihaela van der Schaar (M’99–SM’04–F’10) is currently a ChancellorProfessor of Electrical Engineering with the University of California at LosAngeles, Los Angeles, CA, USA. She holds 33 granted U.S. patents. Herresearch interests include machine learning, data science and decisions formedicine, education, and finance. She received the NSF CAREER Award in2004, the Best Paper Award from the IEEE TRANSACTIONS ON CIRCUITS

AND SYSTEMS FOR VIDEO TECHNOLOGY in 2005, the Okawa FoundationAward in 2006, the IBM Faculty Award in 2005, 2007, and 2008, the MostCited Paper Award from EURASIP Image Communications Journal in 2006,the Gamenets Conference Best Paper Award in 2011, and the 2011 IEEECircuits and Systems Society Darlington Award Best Paper Award. She is amember of the Editorial Board of the IEEE JOURNAL ON SELECTED TOPICS

IN SIGNAL PROCESSING. She received three ISO awards for her contributionsto the MPEG video compression and streaming international standardizationactivities. She is a Distinguished Lecturer of the Communications Societyfrom 2011 to 2012, and the Editor in Chief of the IEEE TRANSACTIONS ON

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