A Coalitional Game Model for Heat Diffusion Based Incentive Routing and Forwarding Scheme.
ABSTRACT We propose an incentive routing and forwarding scheme that integrates a reputation system into a monetary payment mechanism
to encourage nodes cooperation in wireless ad hoc networks. For the first time in the literature, we build our reputation
system based on a heat diffusion model. The heat diffusion model provides us a way of combining the direct and indirect reputation
together and propagating the reputation from locally to globally. Further, we model and analyze our incentive scheme using
a coalitional game, which is not the usual noncooperative game like others. We further prove that under a proper condition
this game has a nonempty stable core. From the evaluation we can see that the cumulative utility of nodes increases when
nodes stay in the core.
 Citations (14)
 Cited In (0)

Conference Paper: Core: a collaborative reputation mechanism to enforce node cooperation in mobile ad hoc networks.
[Show abstract] [Hide abstract]
ABSTRACT: Countermeasures for node misbehavior and selfishness are mandatory requirements in MANET. Selfishness that causes lack of node activity cannot be solved by classical security means that aim at verifying the correctness and integrity of an operation. We suggest a generic mechanism based on reputation to enforce cooperation among the nodes of a MANET to prevent selfish behavior. Each network entity keeps track of other entities' collaboration using a technique called reputation. The reputation is calculated based on various types of information on each entity's rate of collaboration. Since there is no incentive for a node to maliciously spread negative information about other nodes, simple denial of service attacks using the collaboration technique itself are prevented. The generic mechanism can be smoothly extended to basic network functions with little impact on existing protocols.Advanced Communications and Multimedia Security, IFIP TC6/TC11 Sixth Joint Working Conference on Communications and Multimedia Security, September 2627, 2002, Portoroz, Slovenia; 01/2002 
Article: Nuglets: a Virtual Currency to Stimulate Cooperation in SelfOrganized Mobile Ad Hoc Networks
[Show abstract] [Hide abstract]
ABSTRACT: In mobile ad hoc networks, it is usually assumed that all the nodes belong to the same authority; therefore, they are expected to cooperate in order to support the basic functions of the network such as routing. In this paper, we consider the case in which each node is its own authority and tries to maximize the benefits it gets from the network. In order to stimulate cooperation, we introduce a virtual currency and detail the way it can be protected against theft and forgery. We show that this mechanism fulfills our expectations without significantly decreasing the performance of the network.11/2001;  SourceAvailable from: Haixuan Yang
Conference Paper: Mining social networks using heat diffusion processes for marketing candidates selection.
[Show abstract] [Hide abstract]
ABSTRACT: Social Network Marketing techniques employ preexisting social networks to increase brands or products awareness through wordofmouth promotion. Full understanding of social network marketing and the potential candidates that can thus be marketed to certainly offer lucrative opportu nities for prospective sellers. Due to the complexity of so cial networks, few models exist to interpret social network marketing realistically. We propose to model social net work marketing using Heat Diffusion Processes. This paper presents three diffusion models, along with three algorithms for selecting the best individuals to receive marketing sam ples. These approaches have the following advantages to best illustrate the properties of realworld social networks: (1) We can plan a marketing strategy sequentially in time since we include a time factor in the simulation of product adoptions; (2) The algorithm of selecting marketing candi dates best represents and utilizes the clustering property of realworld social networks; and (3) The model we construct can diffuse both positive and negative comments on prod ucts or brands in order to simulate the complicated com munications within social networks. Our work represents a novel approach to the analysis of social network marketing, and is the first work to propose how to defend against nega tive comments within social networks. Complexity analysis shows our model is also scalable to very large social net works.Proceedings of the 17th ACM Conference on Information and Knowledge Management, CIKM 2008, Napa Valley, California, USA, October 2630, 2008; 01/2008
Page 1
A Coalitional Game Model for Heat Diffusion
Based Incentive Routing and Forwarding Scheme
(Work in Progress)
Xiaoqi Li, Wujie Zheng, and Michael R. Lyu
Department of Computer Science and Engineering
The Chinese University of Hong Kong, Shatin, N.T., Hong Kong
{xqli,wjzheng,lyu}@cse.cuhk.edu.hk
Abstract. We propose an incentive routing and forwarding scheme that
integrates a reputation system into a monetary payment mechanism to
encourage nodes cooperation in wireless ad hoc networks. For the first
time in the literature, we build our reputation system based on a heat
diffusion model. The heat diffusion model provides us a way of combining
the direct and indirect reputation together and propagating the reputa
tion from locally to globally. Further, we model and analyze our incentive
scheme using a coalitional game, which is not the usual noncooperative
game like others. We further prove that under a proper condition this
game has a nonempty stable core. From the evaluation we can see that
the cumulative utility of nodes increases when nodes stay in the core.
Keywords: Coalitional Game, Incentive Routing, Heat Diffusion.
1Introduction
The nature of wireless ad hoc networks is to let nodes cooperative together thus
improve the connectivity of the whole network or execute some specific functions
inside the network. However, nodes in this kind of networks may belong to
different individuals or authorities and have their own interests. They may not
want to help others forward routing and data packets, since that will cost their
own energy and bandwidth. Consequently, it is necessary to provide incentive
mechanisms to encourage cooperations among the nodes.
Incentive routing schemes for enforcing selfish agents to cooperate in wireless
networks have been studied for years. One category of solution is using monetary
incentives, either virtually or practically. Payment schemes need to be designed
and usually are analyzed by game theoretic methods. In these schemes, the in
termediate nodes declare their costs for forwarding packages. Then the routing
protocol selects the lowest cost path (LCP) based on the declared costs. After
wards the payments are rewarded to nodes on and sometimes off the LCP with
the amount no less than their declared costs. However, a problem arises when
nodes may purposely declare a higher cost to take advantage of the payment
algorithms. So currently more research is focused on how to avoid cheating and
achieve effective and also economic payments.
L. Fratta et al. (Eds.): NETWORKING 2009, LNCS 5550, pp. 664–675, 2009.
c ? IFIP International Federation for Information Processing 2009
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A Coalitional Game Model665
Another category is employing reputation systems to stimulate the nodes to
cooperative. The common idea of these systems is that each node in the network
will monitor the behaviors of its neighbors. If the neighbors are observed for not
executing some functions properly, their reputations will be decreased and they
will be under the threat of being blocked from the network. The key challenges
are how to combine the direct neighborhood reputations together and propagate
them from locally to globally. In these systems, game theoretic methods can also
be used to analyze the effectiveness of the threatening mechanism. In fact we
consider that the method of using monetary incentives and reputation systems
are not mutually exclusive and they can be combined together to design a more
flexible incentive scheme.
On the other hand, the above schemes are usually modelled as noncooperative
games. However, in wireless networks nodes cannot perform routing and forward
ing behaviors individually. They must cooperate together to complete one task,
so it is natural to think about modelling the wireless network behaviors as a
cooperative game.
In this paper, we are going to model the routing and forwarding procedures
in wireless networks as a cooperative coalitional game with transferable payoff,
and propose an incentive routing and forwarding scheme that combines the idea
of payment mechanism and reputation system together. Then we analyze that
the game has a nonempty core, which is a stable status in cooperative game
just like the Nash Equilibrium in a noncooperative game.
Regarding the combination of reputation and payment schemes, we first need
to obtain a combined and globalized reputation, and then smoothly map this
reputation value to a certain amount of payment. On the basis of it, we also
need to design an incentive payment scheme integrating reputation and cost
together. In the formulation of a coalitional game the key challenges are: 1) how
to write the value function of the coalition which represents the collective payoff
of the coalition; 2) how to find the solution of this game where every node has a
satisfying payoff share, so that it will not deviate from some stable status. Some
games may not have such a stable solution. The objective of our paper is to solve
the above questions.
We list our major contributions as follows: First, we design an incentive rout
ing and forwarding scheme that integrates reputation information into a payment
mechanism. Second, we introduce a heat diffusion model to combine the direct
and indirect reputations together and propagate them from locally to globally in
the way how heat diffuses. Third, unlike others, we model this incentive scheme
using a coalitional game method. A characteristic value function of the coalition
is designed, and we prove that this game has a core solution.
The rest of this paper is organized as follows. We first give the background of
the heat diffusion model in Section 2. After describing some technical prelimi
naries in Section 3 we will propose our incentive routing and forwarding scheme
in Section 4. The scheme is analyzed in Section 5, then we show some evaluation
results in Section 6. In the end, some related work and conclusions are given in
Section 7 and Section 8 respectively.
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666X. Li, W. Zheng, and M.R. Lyu
2Background of Heat Diffusion Model on Weighted
Directed Graph
2.1Motivation
A reputation system usually needs to address two problems: 1) how to combine
subjective direct reputations with indirect reputations from neighbors to make
them become more objective; and 2) how to propagate the reputation from
locally to globally. Previously there are different solutions to these problems
such as [1] and [2]. In this work, we will employ the heat diffusion model to
fulfill the requirements.
In nature, heat always flows from high temperature positions to low temper
ature positions via conductive media. A heat diffusion model describes this phe
nomenon that heat can diffuse from one point to another through an underlying
manifold structure in a given time period. The higher the thermal conductiv
ity of the medium, the easier the heat flows, which implies that the two end
points have some cohesive relations. Diffusion behaviors are also affected by the
underlying geometric structures. Some achievements have been made based on
the heat diffusion model such as classification in machine learning field, page
ranking in information retrieval [3] and marketing candidates selection in social
computing [4], but to our best knowledge, there is no previous work that has
been performed on the incentive routing in wireless networks.
We see that in the process of heat diffusion, each node’s heat comes from all
of its incoming links and diffuses out to its successors as long as it can. If we
diffuse heat on a weighted directed graph, the amount of heat a node can get
depends not only on the heat of its neighbors but also on the weights of the
links connecting them. The higher the weight, the more thoroughly the heat can
be diffused. Therefore, if we let the weight be the direct reputation value of the
link, then the amount of heat will be the overall reflection of the underlying
reputation information. The course of heat diffusion through all possible links
can also be deemed as a propagation of the reputations.
2.2Heat Diffusion on Weighted Directed Reputation Graph
We construct a heat diffusion model on the reputation graph G = (M,E,R),
where M = {1,2,...,m} is the node set. E = {(i,j) i and j are in communication
range and the transmission direction is from i to j}. The heat only flows from i
to j if (i,j) ∈ E. R is the reputation set {rij rijis the direct reputation of edge
(i,j)}. We use fi(t) to describe the heat value of node i at time t, beginning
from an initial distribution of heat fi(0) at time zero. f(t) denotes the vector
consisting of fi(t).
The heat diffusion modelling is as follows. Suppose, at time t node i diffuses
HD(i,t,Δt) amount of heat to its subsequent nodes. We assume that: a) the
heat HD is proportional to the time period Δt; b) HD is proportional to the
heat of node i; c) each node has the same ability to diffuse heat; and d) node i
intends to distribute HDuniformly to each of its subsequent nodes, but the actual
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A Coalitional Game Model667
heat it can diffuse is proportional to the corresponding reputation weight of the
edge. On the basis of the above considerations, we state that node i will diffuse
λpikfi(t)Δt/liamount of heat to each of its subsequent node k, where liis the
outdegree of node i and λjis the thermal conductivity, which is the heat diffusion
coefficient representing the heat diffusion ability. In the case that the outdegree
of node i is zero, we assume that this node will not diffuse heat to others. Then
the total amount of heat node i will diffuse is?
j during a period of Δt. We also have the following assumptions: a) HR is
proportional to the time period Δt; b) HRis proportional to the heat of node j; c)
HRis zero if there is no link from node j to i. Based on the above considerations,
we obtain HR(i,j,t,Δt) = λjfj(t)Δt. As a result, the heat that node i receives
between time t and t + Δt will be equal to the sum of the heat flowing from
all its neighbors pointing to it, which is?
have λpjifj(t)Δt/lj= λjfj(t)Δt. So we get λj= λpji/lj. To sum up, the heat
difference at node i between time t and t + Δt will be the amount of heat it
receives deduced by what it diffuses. The formulation is therefore:
k:(i,k)∈Eλpikfi(t)Δt/li.
On the other hand, each node i receives HR(i,j,t,Δt) amount of heat from
j:(j,i)∈Eλjfj(t)Δt. Since the amount
of heat that j diffuses to i should be equal to the amount i receives from j, we
fi(t + Δt) − fi(t) = λ
⎛
⎝
?
j:(j,i)∈E
pji
lj
fj(t) − μi
?
k:(i,k)∈E
pik
li
fi(t)
⎞
⎠Δt,
(1)
where μiis a flag to identify whether node i has any outlinks. If node i does not
have any outlinks, μi= 0; otherwise, μi= 1. To find a closed form solution to
Eq.(1), we then express it in a matrix form:
f(t + Δt) − f(t)
Δt
⎧
⎩
= λHf(t),where(2)
Hij=
⎨
pji/lj,
−(μi/li)?
(j,i) ∈ E,
i = j,
otherwise.
k:(i,k)∈Epik,
0,
(3)
Solving the above equation, we get
f(t) = eλtHf(0) (4)
The matrix eλtHis called the diffusion kernel, showing that the heat diffusion
process continues infinite times from the initial heat diffusion step.
3Technical Descriptions
Before presenting our incentive scheme and coalitional game we first give some
technical notations. Our game is based on the bidirectional weighted graph
G = (M,E,P) described in Section 2. Suppose that s is the source node and
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668X. Li, W. Zheng, and M.R. Lyu
Fig.1. Illustration of Notations of the Coalitional Game
d is the destination node, then the player set of this coalitional game is N =
M \{s,d}. Coalition is denoted by any nonempty subset T ⊆ N, and the overall
payoff of the coalition is denoted by v(T) ∈ R. Then the game is expressed by
Γ =< N,v >. Players will form into coalitions to help establishing the highest
effective path between s and d with the lowest cost under the constraint that each
intermediate node’s heat is higher than a threshold θ. If there’s a tie in the total
cost, s will break the tie by choosing the path with the highest heat. The source
can freely choose the value of θ to meet its requirement on reputation. The larger
the value θ is, which means the source has a higher demand on reputations, the
higher payments it will expend. All the paths established inside the coalition T
connecting s and d compose the path set Psd(T).
Initially, s will load a certain amount of initial heat f(0) and diffuse it on
the reputation graph, then at time t, each node will be diffused fi(t) amount
of heat. Correspondingly each source s has an initial balance of h(0), and the
payment to each node hi(t) is paid by it according to fi(t). Every node evolving
in the routing or forwarding procedure will cost its energy. Since the cost for
sending/receiving routing and data packets are different [5], and the cost for
data transmission is usually larger than that of routing packets transmission, we
denote the routing and forwarding cost respectively by ci(r) and ci(f) ∈ R+,
and ci(r) < ci(f) for all i ∈ N. Please see Fig. 1 for the illustration of notations.
4 Incentive Routing and Forwarding Scheme
The basic idea of achieving incentives is that nodes will be paid when they
help others forwarding data or routing packets. Unlike other payment schemes
that reward the nodes according to their claimed cost, our incentive routing and
forwarding scheme pays the nodes by their reputations. The higher a node’s
reputation is, the higher payment it can get. The payment is given by the source
node. The payment may be in the form of virtual currency like [6] or any other
practical form. In our paper we assume that there is such a payment form and
a payment operation daemon in the network.
In the scheme, the source node s will originate the heat diffusion process start
ing from itself. Then after collecting the forwarding cost of all the
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A Coalitional Game Model669
Algorithm 1. Incentive Routing and Forwarding Scheme
Input: Source s, destination d, reputation graph G, and heat threshold θ
Output: HEPN
foreach i ∈ N do
i claim its forwarding cost ci(f) to s;
2
fi(0) = 0;
3
1
fs(0) = f(0);
Execute the heat diffusion process f(t) = eλtHf(0);
s chooses the highest effective path to d with the lowest cost, subject to
fi(t) ≥ θ. If there is a tie, s selects the one with the highest heat;
... Data transmission process; ...
s pays hi(t) to each i according to fi(t);
s adjusts its heat threshold θ;
Updates reputation graph G;
4
5
6
7
8
9
10
players, s will compute the lowest cost path under the constraint that the dif
fused heat of each intermediate node is higher than its assigned threshold θ. We
call this path as the highest effective path (HEP). Selfish or unreliable nodes will
be degraded with respect to their direct reputations by their neighbors while en
thusiastic or reliable nodes will be upgraded in their reputations. The extent of
increasing or decreasing a node’s reputation depends on the functions it takes.
Forwarding data packets will get higher reputation increments than forwarding
routing packets. Correspondingly, not forwarding data packets will get heavier
punishment on reputation than not forwarding routing packets. The utility a
node gets in one session is the amount of payment it receives from the source
node, subtracted by the cost it expends for forwarding data or routing packets.
The scheme is summarized in Algorithm 1.
Under the effect of the algorithm, we can see that by behaving cooperatively
a node can get higher and higher reputations, thus the payment to it will also
be increased, so as to the individual utility. To earn more utility, the node will
then try to improve its reputation by actively forwarding for others.
Sometimes for one session a node’s utility obtained for forwarding routing
packets may be higher than that of forwarding data packets. But the increasing
acceleration of the latter is larger than that of the former because of the different
updating way of reputation. So in the long run the cumulative utility of the node
in the latter will exceed that in the former. If a node declare a higher cost than
its actual forwarding cost to avoid being selected in the HEP, it will suffer the
same situation. The above are some intuitive thoughts behind the scheme; for
precise analysis we give it in Section 5.
5Our Coalitional Game
In this section we will analyze the proposed incentive scheme by modelling
the routing and forwarding procedure as a cooperative coalitional game with
transferable payoff. Furthermore, we show that the game has a nonempty core.
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670 X. Li, W. Zheng, and M.R. Lyu
5.1 Value Function of the Coalition
The value or characteristic function is the key component of a coalitional game.
For each coalition T, the value v(T) is the total payoff that is available for division
among the members of T. It can also be interpreted to be the most payoff that the
coalition T can guarantee independent of the behavior of the coalition N \T [7].
Now we will define the value function of the coalition in our game. As described
in Section 3, s is the source node and d is the destination node. The player
set is N = M \ {s,d}. When nodes join together into one coalition, they will
establish one or more paths between s and d, each of which gives the coalition
a collective payoff wP(T), where P ⊆ T represents a path. The collective payoff
comes from each member’s contributions of their reputationbased payments hi,
then subtracted by the costs they bear for performing routing or forwarding
behaviors. For those who are only involved in the routing discovery process the
cost is ci(r), and for those who have been selected in a path the cost should be
ci(f). So for each path P ⊆ T, the corresponding payoff function for the coalition
is wP(T) =?
maximal collective payoff it can guarantee, which is:
⎛
i∈T
We call the path that has the maximal wP(T) as the highest effective path
HEPT, so alternatively we can write v(T) =
?
the definition of v(T) as follows.
i∈Thi−?
i∈Pci(f)−?
i?∈Pci(r). Among all these payoffs, we say
that the characteristic worth or the value of the coalition v(T) should be the
v(T) = max
P⊆T
⎝?
hi−
?
i∈P
ci(f) −
?
i?∈P
ci(r)
⎞
⎠.
(5)
?
i∈Thi−?
i∈HEPTci(f) −
i?∈HEPTci(r). But if there is no such path inside the coalition, the coalition is
inessential and worths nothing, and the value of it is 0. Then formally, we have
Definition 1 (Value Function of A Coalition). The value of any coalition
T ⊆ N is 0 when there is no path between s and d inside T. That is: v(T) = 0,
if Psd(T) = φ. Otherwise, v(T) is:
?
v(T) =
i∈T
hi−
?
i∈HEPT
ci(f) −
?
i?∈HEPT
ci(r),
if Psd(T) ?= φ
(6)
5.2Nonemptiness of the Core
The key issue of a cooperative game is regarding how to divide earnings inside the
coalition in some effective and fair way. The adequate allocation profile is then
called a solution, which is a vector x ∈ RNrepresenting the allocation to each
player when a grand coalition is formed. The grand coalition means all the players
form into one coalition. The core is one of the solution concepts for cooperative
games. If a coalitional game’s core is nonempty, it means that no coalition can
obtain a payoff that exceeds the sum of its members’ current payoffs, which
Page 8
A Coalitional Game Model 671
means no deviation is profitable for all of its members [7]. Theoretically the core
is the set of imputation vectors which satisfies the following three conditions:
1. x(i) ≥ v(i)
2. x(T) ≥ v(T), ∀T ∈ 2N
3. x(N) = v(N), N is the player set
(7)
where x(i) is the payoff share of node i in this game, x(T) =?
The core of a coalitional game is possibly empty. Next we will analyze in
which condition our game has a nonempty core, and what the possible core is.
We derive the following theorem.
i∈Tx(i), and
x(N) =?
i∈Nx(i).
Theorem 1. Under the condition of hi ≥ ci(f) for each player i, the payoff
profile x is in the core of the coalitional game where
?hi− ci(f),
Proof. Firstly, check the first requirement of Eq.7. Under the condition of hi≥
ci(f), we have x(i) = hi−ci(f) ≥ 0. When the coalition has only one member i,
the value of it would be 0 if i cannot establish a path between s and d. That is
v(i) = 0. Thus x(i) ≥ v(i) holds. If i can connect s and d, then v(i) = hi−ci(f)
as said by Def.1. In that case x(i) = v(i) which also meets the first requirement.
Secondly, from Eq.8 and Def.1, we have x(N) =?
v(N). So the third requirement of Eq.7 also holds.
Thirdly, to prove x satisfies the second requirement x(T) ≥ v(T), we will list
and analyze all of the different HEP situations in the grand coalition N and an
arbitrary coalition T. For those coalitions without paths inside, the values of
them are 0, so we easily get x(T) ≥ v(T) = 0. For other coalitions, there are
totally four kinds of situations as illustrated in Fig.2.
The proof for these four situations are similar. Because of the space limit, we
only prove the most complicated situation in Fig.2(d) here. In this case, when
the grand coalition N is formed, the new HEPN is different from HEPT and
part of HEPN is inside T. For clarity we first give the following notations for
Fig.2(d). We let A = HEPN∩ T, B = HEPN∩ (N \ T), C = HEPT ∪ A,
x(i) =
i ∈ HEPN
i ?∈ HEPN
hi− ci(r),
(8)
i∈Nx(i) =?
i∈HEPN(hi−
i?∈HEPNci(r) =
ci(f))+?
i?∈HEPN(hi−ci(r)) =?
i∈Nhi−?
i∈HEPNci(f)−?
(a)(b)(c)(d)
Fig.2. Examples of Different HEP Situations
Page 9
672X. Li, W. Zheng, and M.R. Lyu
D = T \ C, and E = N \ (HEPN∪ HEPT). According to Def.1 and Eq.8, we
have:
?
i∈HEPT
HEPN and HEPT are two paths connecting s and d inside the grand coalition
N, and HEPN dominates HEPT. So based on Eq.5, we have vHEPN(N) ≥
vHEPT(N). Through deduction we get:
x(T) − v(T) =
?
ci(f) −
?
i∈HEPT
ci(r)
?
−
??
i∈A
ci(f) −
?
i∈A
ci(r)
?
(9)
?
i∈HEPT
ci(f) −
?
i∈HEPT
ci(r) ≥
??
i∈A
ci(f) −
?
i∈A
ci(r)
?
+
??
i∈B
ci(f) −
?
i∈B
ci(r)
?
>
?
i∈A
ci(f) −
?
i∈A
ci(r)
Then substitute in Eq.9, we get x(T) ≥ v(T). So the second requirement is
satisfied. In summary, under the condition of hi≥ ci(f) for each player i, the
proposed payoff profile x is in the core of this coalitional game.
? ?
We can see that if only the payment a node gets based on its reputation is larger
than the cost it needs to forward data packets, the core of this coalitional game
exists. Nodes who want to get more payoff share xi must try to improve its
reputation by helping others forwarding or increasing its link reliability, so that
it can get more diffusion of the heatbased payment. In this way a virtuous cycle
can be created.
6Evaluations
We have theoretically proved that our incentive scheme guarantees the existence
of the core when modelled as the coalitional game. Now we will evaluate the
scheme in two aspects through experiments: 1) how is the general overview of
all the nodes’ utility and how does the network topology affect the distribution
of it; and 2) how the nodes’ cumulative utilities and balances evolve over time.
We conduct the evaluation on a randomly generated wireless topology with
100 nodes scattering in an area of 3000 by 3000 meters. The radio range is set to
422.757 meters. The topology is shown in Fig.3(a). There is a line connecting two
nodes when they are in the communication range of each other. We label some
representative nodes for further illustration. Each node has an initial balance of
100 and each directed link has a local reputation value as the weight. At each
round we randomly select a sourcedestination pair and the source s perform
the incentive routing and forwarding algorithm. We assign the parameter λ in
Page 10
A Coalitional Game Model 673
0500 1000150020002500 3000
0
500
1000
1500
2000
2500
3000
40
44
100
22
87
1
42
(a)
0500 1000 1500200025003000
0
500
1000
1500
2000
2500
3000
40
44
100
22
87
1
42
(b)
Fig.3. Network Topology and Overview of Nodes’ Utilities
the heat diffusion equation as 1. The evaluation runs for 1000 seconds and we
observe the utility and balance of each node every second.
Our first evaluation shows the overview utility at the end of the experiment
in Fig.3(b). The circles around the nodes represent the cumulative utility of that
node. The diameter of the circle is proportional to the amount of the utility.
We observe that in general nodes in the high density area also have large
circles around them (like node 44), and on the contrary, nodes in the sparse area
usually have indistinctive circles.
Our second evaluation starts from the core of the coalitional game. Fig.4(a)
and 4(b) show the cumulative utilities and balances of several typical nodes
respectively over the simulation time. The balance of a node may fall below the
initial balance (like node 42) because the nodes have their own data transmission
requests and what they earn cannot compensate what they pay.
0 200 400600 8001000
0
50
100
150
200
250
300
350
400
Time (s)
Cumulative Utility
node 87
node 22
node 100
node 44
node 40
node 42
node 1
(a)
0 200400 6008001000
0
50
100
150
200
250
300
350
400
450
500
Time (s)
Balance
node 87
node 22
node 100
node 44
node 40
node 42
node 1
(b)
Fig.4. Cumulative Utility and Balance of Nodes as a Function of Simulation Time
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674X. Li, W. Zheng, and M.R. Lyu
7 Related Work
Many incentive routing schemes have been proposed in the past few years. Most
approaches fall into one of two main categories. In the first category, nodes for
warding packets get monetary incentives for their service. In Ad HocVCG [8],
payments are paid to nodes consisting the actual costs incurred by forwarding
data and the extra premiums. The implemented reactive routing protocol is a
variation of the wellknown VCG mechanism. It achieves the design objectives
of truthfulness and costefficiency in a gametheoretic sense. Another work [6]
introduces a virtual currency called nuglets. The source of the packet must load
it with enough nuglets to pay for the trip to the destination. Cooperation is
enforced in this scheme because nodes must forward packets for others in order
to build up enough nuglets to get their own packets forwarded. [9] designs an
incentivecompatible routing and forwarding protocol integrating VCG mecha
nism and cryptographic technique. Payments are implemented based on VCG
protocol and the application of cryptographic techniques in the design of for
warding protocol enforces the routing decision. [10] designs a collusionresistant
routing scheme for noncooperative wireless networks. Payments are given to
nodes not only on the LCP paths but also off the paths.
In the second category, noncooperative nodes are identified based on a rep
utation system and circumvented in the routing process. In CORE [1], node
cooperation is stimulated by a collaborative monitoring technique and a reputa
tion mechanism. Each node of the network monitors the behavior of its neighbors
with respect to a requested function and collects observations about the execu
tion of that function. CONFIDANT [11] differs from CORE only in that it sends
reputation values to other nodes in the network, which exposes the scheme to
malicious spreading of false reputation values. Liu and Issarny employ a Bayesian
approach to design an incentive compatible reputation system to facilitate the
trustworthiness evaluation of nodes [12]. Some also use subjective logic to cal
culate uncertain trust so as to design secure routing protocols [2] or incentive
reputation mechanisms [13].
8 Conclusion and Future Work
In this paper, we present a novel incentive routing and forwarding scheme which
combines reputation system and payment mechanism together to encourage
nodes to cooperate in wireless ad hoc networks. Besides, we design our repu
tation system based on a heat diffusion model for the first time in the literature.
The heat diffusion model provides us a way of combining the direct and indirect
reputations together and propagating the reputation from locally to globally.
Further, instead of using the noncooperative game method, we model and ana
lyze our incentive scheme using a coalitional game. We further prove that under
a certain condition this game has a nonempty core. Through the evaluation we
can see that the cumulative utility of nodes increases when the nodes stay in the
core. In the future we will consider to apply other underlying reputation systems
to our incentive scheme.
Page 12
A Coalitional Game Model 675
Acknowledgement
The work described in this paper was fully supported by a grant from the Re
search Grants Council of the Hong Kong Special Administrative Region, China
(Project No. CUHK4158/08E).
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