A Contract-based Incentive Mechanism for Energy Harvesting-based Internet of Things
aa r X i v : . [ c s . G T ] M a r A Contract-based Incentive Mechanism for EnergyHarvesting-based Internet of Things
Zhanwei Hou ∗ , He Chen ∗ , Yonghui Li ∗ , Zhu Han † , and Branka Vucetic ∗∗ School of Electrical and Information Engineering, University of Sydney, Sydney, NSW 2006, AustraliaE-mail: { zhanwei.hou, he.chen, yonghui.li, branka.vucetic } @sydney.edu.au † Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77004-4005 USAE-mail: { [email protected] } Abstract —By enabling wireless devices to be charged wire-lessly and remotely, radio frequency energy harvesting (RFEH)has become a promising technology to power the unattendedInternet of Things (IoT) low-power devices. To enable this,in future IoT networks, besides the conventional data accesspoints (DAPs) responsible for collecting data from IoT devices,energy access points (EAPs) should be deployed to transferradio frequency (RF) energy to IoT devices to maintain theirsustainable operations. In practice, the DAPs and EAPs maybe operated by different operators and a DAP should providecertain incentives to motivate the surrounding EAPs to charge itsassociated IoT device(s) to assist its data collection. Motivated bythis, in this paper we develop a contract theory-based incentivemechanism for the energy trading in RFEH assisted IoT systems.The necessary and sufficient condition for the feasibility ofthe formulated contract is analyzed. The optimal contract isderived to maximize the DAP’s expected utility as well as thesocial welfare. Simulation results demonstrate the feasibility andeffectiveness of the proposed incentive mechanism.
I. I
NTRODUCTION
By connecting objects, physical devices, vehicles, animalsand other items without human intervention, Internet of Things(IoT) has emerged as a new paradigm to enable ubiquitousand pervasive Internet connections [1]. Wireless sensing andmonitoring service is one of the fundamental applications ofIoT, which enables systems and users to continually monitorambient environment.One of the major hurdles for implementing the wirelesssensing application is the limited lifetime of traditional battery-powered sensors, which are costly and hard to maintain.For example, frequent recharging or battery replacement isinconvenient in deserts or remote areas, and is even impossiblefor some scenarios, such as toxic environment or implantedmedical applications [2]. To tackle this problem, radio fre-quency energy harvesting (RFEH) has recently been proposedas an attractive technology to prolong the operational lifetimeof sensors, enhance the deployment flexibility, and reduce themaintenance costs [2], [3].In this paper, we consider a RFEH-based IoT system con-sisting of a data access point (DAP) and several energy accesspoints (EAPs). The DAP is in charge of collecting informationfrom its associated sensors. The sensors are assumed to haveno embedded energy supply, but they can harvest energy fromradio frequency (RF) signals radiated by the surrounding EAPsto transmit the data to the DAP. In practice, the DAP and EAPs may be operated by different operators. To successfullymotivate these third-party and self-interested EAPs to helpcharge the sensors, effective incentive mechanisms should bedesigned to improve the payoff of the DAP as well as thoseof EAPs.Traditionally, the devices belonging to the same networkwith extra energy were assumed to voluntarily assist otherdevices, e.g., [4]. However, this becomes no longer applica-ble for the considered system with self-interested third-partyEAPs, as these EAPs tend to maximize their own benefits. In[5], an incentive mechanism was designed for the system withthe similar setup where monetary rewards were provided bythe DAP to motivate third-party EAPs to assist the chargingprocess. This process was referred to as “energy trading”.The authors formulated the incentive problem as a Stackelberggame, where the DAP is the buyer for the RF energy and theEAP competes to sell energy to the DAP. Another auction-based incentive mechanism was developed and evaluated in[6] for an alternative energy trading scenario with multipleDAPs and a single EAP. In these schemes, it was assumed thatthe EAP(s) will truthfully report some private information tothe DAP(s), e.g., their energy costs and channel gains betweenEAPs and sensors. However, this assumption is not realistic.Since EAPs are selfish, in practice, an EAP may provide mis-leading information maliciously and pretend to be an EAP withbetter channel condition and/or higher energy cost to cheat formore rewards. A malicious EAP can succeed in cheating toget more benefits because of information asymmetry in theenergy trading process. Specifically, an EAP clearly knows itsprivate information, such as its own energy cost and channelconditions towards sensors to be charged, which are generallyhard to be known by the DAP. To address this issue, in thispaper we will design an effective incentive mechanism tomaximize the expected utilities of the DAP and EAPs byovercoming the information asymmetry. We are interested inaddressing following questions without knowing the privateinformation of EAPs:
Which EAPs the DAP should hire, howmuch energy should be requested from the hired EAPs, andhow many rewards should be given to the hired EAPs?
To answer the above questions, we apply the well-established contract theory to design the incentive mechanismof the energy trading process in the considered RFEH-basedIoT system. Contract theory is an powerful tool originatedfrom economics to model the incentive mechanism under information asymmetry in a monopoly market. This problemsis called “adverse selection” in contract theory [7]. It has beenemployed to address incentive design problems in wirelesscommunication areas, such as device-to-device (D2D) com-munications [8] and cooperative spectrum sharing [9]. To thebest knowledge of the authors, this is the first work that usescontract theory to design the incentives for the energy tradingprocess in RFEH-based IoT systems.In our design, the energy trading market is analogous asa monopoly market in economics. The DAP is the employerwho offers a contract to each EAP. The contract is composedof a serious of contract items, which are combinations ofenergy-reward pairs. Each contract item is an agreement abouthow many rewards an EAP will get by contributing howmuch energy. Various heterogeneous EAPs are classified intodifferent types according to their energy costs and instanta-neous channel conditions. The EAPs are regarded as labors inthe market, which will choose a contract item best meetingtheir interests. By properly designing the contract, an EAP’stype will be revealed by its selection. Thus the DAP cancapture each EAP’s private information to a certain extent andthus overcome the issue of information asymmetry. Duringthe design of the contract, we characterize the necessaryand sufficient conditions for the contract feasibility, i.e, in-dividual rationality (IR) conditions and incentive capability(IC) conditions. Subject to the IR and IC constraints, theoptimal contract under information asymmetry is derived bymaximizing the DAP’s expected utility as well as the socialwelfare. Simulations validate the feasibility and effectivenessof the proposed incentive mechanism.II. S
YSTEM M ODEL
We consider one DAP and N EAPs belonging to differentoperators, which are connected to constant power supplies. TheDAP is responsible for collecting various data from severalwireless-powered sensors within its serving region. Withoutembedded energy supplies, the wireless-powered sensors fullyrely on the energy harvested from the RF signals emitted bythe EAPs to transmit its information to the DAP. For simplicity,we consider that the RF energy transfer and information trans-mission are performed over orthogonal bandwidth. Since theEAPs are assumed to belong to different operators, they cannotcollude with each other, i.e., energy trading among EAPs isnot considered. For analytical tractability, time division-basedtransmission among sensors is adopted, i.e., there is only oneactive sensor during each transmission block. Hereafter, werefer to this active sensor as the information source. Besides,all the nodes in the system are assumed to be equipped withsingle antenna and operate in the half-duplex mode.The DAP will offer a contract to effectively motivate theEAPs to charge its information source (i.e., the active sensor).In practice, the EAPs can be heterogeneous with differentenergy costs and instantaneous channel gains towards the in-formation source. Obviously, there is asymmetric informationbetween the DAP and EAPs. To be more precise, each EAPknows exactly its energy cost and channel status , which is, Note that each EAP can estimate its channel towards the sensor via theuplink pilots sent by the sensor. however, unknown to the DAP. To overcome this informationasymmetry, the DAP will design a group of energy-rewardcontract items. Rewards can be monetary incentive or freeoffloading data between operators.We consider that the energy-carrying signals sent by theEAPs are independent and identically distributed (i.i.d.) ran-dom variables with zero mean and unit variance. Note that nocoordination between the EAPs is needed since independentsignals are transmitted. All channels are assumed to experienceindependent slow and flat fading, where the channel gainsremain constant during each transmission block and changeindependently from one block to another. The informationsource rectifies the RF signals received from the EAPs anduses the harvested energy to transmit its information. The timeduration of every transmission block is normalized to one. Sowe use “energy” and “power” interchangeably hereafter. Theamount of energy harvested by the information source duringone transmission block can be expressed as E s = η N X m =1 p m G m,s , (1)where < η < is the energy harvesting efficiency, p m isthe charging power of the m th EAP, and G m,s is the channelpower gain between the m th EAP and the information source.Note that the noise is ignored in (1) since it is practicallynegligible at the energy receiver.The harvest-use protocol is considered in this paper [10].More specifically, the information source will use the har-vested energy to perform instantaneous information transmis-sion to the DAP. We consider a battery-free design whichindicates that the sensor only has a storage device like su-percapacitor to hold the harvested energy for a short period oftime, e.g., among its scheduled transmission block. Hence thesensor exhausts all the harvested energy in each transmissionblock, so the sensor’s energy storage device is emptied atthe beginning of the transmission block. This battery-freedesign can reduce the complexity and costs of the sensors,which is particularly suitable for the considered IoT sensingapplications and has been adopted by other applications [11],[12]. The transmit power of the information source is P s = E s . (2)Then, the received signal-to-noise ratio (SNR) at the DAP is β = p s G a,s N , (3)where N is the noise power at the DAP, and G a,s is thechannel power gain from the information source to the DAP.Hence the achievable throughput (bps) from the informationsource to the DAP can be expressed by R sa = W log (1 + β )= W log ηG a,s N N X m =1 p m G m,s ! , (4) where W is the bandwidth. We define the received power con-tributed by the m th EAP as q m = p m G m,s and γ = ηG a,s /N for notation simplicity. So (4) is simplified as R sa = W log γ N X m =1 q m ! . (5)In the following subsections, we will define the utilities ofthe DAP and EAPs as well as the social welfare. A. DAP’s Utility
Note that the aim of the DAP is to pay less rewards to theEAPs to achieve higher throughput. The DAP’s utility can thusbe defined as U DAP = W log γ N X m =1 q m ! − c N X m =1 π m , (6)where π m is the money (or amount of free offloading data)paid by the DAP to the m th EAP for its correspondingcontribution q m , and c is the unit cost of the DAP, whichis normalized as c = 1 without loss of generality. B. EAPs’ Utilities
The utility of the k th EAP is defined as U k = π k − C k ( p k ) , (7)where p k = q k /G k,s is the transmit power of the k th EAP,and C k ( · ) is used to model the energy cost of the k th EAP,given by C k ( x ) = a k x , (8)where a k > . Note that the above quadratic function hasbeen widely adopted in the energy trading market to modelthe energy cost [13]. Equivalently, (7) can be rewritten as U k = π k − a k G k,s q k . (9)We define the type of the k th EAP as θ k := G k,s a k , (10)which suggests that the stronger the channel quality G k,s between the EAP and the information source, and/or the lowerthe unit power cost a k , the higher the type of the EAP. Withoutloss of generality, we assume that there are totally K types ofEAPs with θ < θ < · · · < θ K . In this definition, the highertype EAP has better channel quality and/or lower energy cost.Note that since a k > and G k,s > , θ > holds. Using(10), the EAP’s utility can be rewritten as U k = π k − q k θ k . (11)Assume there are N k EAPs belonging to the k th type, we thushave P Kk =1 N k = N . We then can rewrite the DAP’s utilityaccording to the types of EAPs as U DAP = W log γ K X k =1 N k q k ! − K X k =1 N k π k . (12) C. Social Welfare
The social welfare is defined as the summation of theutilities of the DAP and all N EAPs, given by
Γ = U DAP + K X k =1 N k U k = W log γ K X k =1 N k q k ! − K X k =1 N k q k θ k . (13)It can be seen that the internal transfers, i.e., rewards, arecancelled in the social welfare, which is consistent withthe aim to maximize the efficiency of the whole system,i.e., achieving more throughput at the cost of less energyconsumptions.III. C ONTRACT F ORMULATION
In this section, we will formulate a contract for the energytrading between the DAP and EAPs, characterize its feasibilityconditions, and derive the optimal contract subject to thefeasibility conditions.To overcome the information asymmetry, a contract includ-ing a series of energy-reward pairs ( q k , π k ) (i.e., contract item)is designed to maximize the expectation of the DAP’s utility,which is consistent with the social welfare in our model. Forthe k th type EAP, q k is the received power contributed by k thEAP and π k is the money paid to the k th EAP as the rewardfor its contribution. A. Optimal Contract with Asymmetric Information
Generally, the first step in a contract design is to figureout its feasibility conditions. In our design, to encourage theEAPs to participate in the charging process and ensure thateach EAP only chooses the contract item designed for itstype, the following individual rationality (IR) and incentivecompatibility (IC) constraints should be satisfied [7].
Definition 1: Individual Rationality (IR).
The contract itemthat an EAP chooses should ensure a nonnegative utility, i.e., U k = π k − q k θ k ≥ , ∀ k ∈ { , . . . , K } . (14) Definition 2: Incentive Compatibility (IC).
An EAP of anytype k prefers to choose the contract item ( q k , π k ) designedfor its type, instead of any other contract item ( q j , π j ) , ∀ j ∈{ , . . . , K } and j = k , given by π k − q k θ k ≥ π j − q j θ k , ∀ k, j ∈ { , . . . , K } . (15)The IR condition requires that the received reward of eachEAP should compensate the cost of its consumed energy whenit participates in the energy trading. If U k ≤ , the EAP willchoose not to charge the information source for the DAP.We define this case as ( q k = 0 , π k = 0) . The IC conditionensures that each EAP automatically selects the contract item Note that the received power contributed by each EAP is assumed tobe distinguishable by considering that the EAPs work in disjoint narrowbandwidth. designed for its corresponding type. The type of each EAPis thus revealed to the DAP, which is called “self-reveal”. Ifa contract satisfies the IR and IC constraints, we refer to thecontract as a feasible contract.In this paper, we consider a scenario with strong informationasymmetry. In such a scenario, the DAP is only aware of thetotal number of EAPs (i.e., N ) and the distribution of eachtype. But it does not know the exact number of each type k (i.e., N k ). So the DAP needs to optimize its expected utilityover the possibilities of all possible combinations of N k . Theexpected utility of the DAP with N EAPs is given by E { U DAP } = N X n =0 N − n X n =0 · · · N − P K − i =0 n i X n K − =0 ( Φ n ,...,n K " W log γ K X k =1 n k q k ! − K X k =1 n k π k , (16)where Φ n ,...,n K is the probability of a certain combination ofthe number of EAPs belonging to each type (i.e., N k , { k =1 , , . . . , K } ) and n K = N − P K − i =0 n i is known after giving n , n , . . . , n K − since the DAP knows the total number N of EAPs. We assume that all types are uniformly distributed,so the probability of one EAP belonging to each type is thesame, which is /K . In this case, Φ n ,...,n K can be calculatedas Φ n ,...,n K = Pr ( N = n , N = n , . . . , N k = n k )= N ! n ! n ! . . . n K ! K N (17)Recall that the DAP aims at maximizing its expected utilitysubjecting to the constraints of IR and IC given in (14) and(15). Thus, the optimal contract becomes max ( q k ,π k ) E { U DAP } s.t. π k − q k θ k ≥ , ∀ k ∈ { , . . . , K } ,π k − q k θ k ≥ π j − q j θ k , ∀ k, j ∈ { , . . . , K } ,q k ≥ , π k ≥ , θ k ≥ , ∀ k ∈ { , . . . , K } . (18)The first two constraints correspond to IR and IC, respectively.Note that the EAP will reveal its private type truthfullywith the IR and IC constraints. Specifically, the IR conditionensures the EAP’s participation and the IC condition ensuresthat each EAP selects the contract item designed for itscorresponding type to gain highest payoff. B. Problem Transformation
There are K IR constraints and K ( K − IC constraintsin (18), which are non-convex and couple different EAPstogether. It is hard to solve (18) directly due to the complicatedconstraints. Motivated by this, in the subsection we first reducethe constraints of (18) and transform it.We first realize that the following necessary conditions canbe derived from the IR and IC constraints.
Lemma 1:
For any feasible contract, π i > π j if and onlyif q i > q j , ∀ i, j ∈ { , . . . , K } and π i = π j if and only if θ i = θ j , ∀ i, j ∈ { , . . . , K } . Lemma 2:
For any feasible contract, π i = π j if and only if θ i = θ j , ∀ i, j ∈ { , . . . , K } . Lemma 3:
For any feasible contract, if θ i > θ j , then π i >π j , ∀ i, j ∈ { , . . . , K } .Note that the proof for Lemma 1 to Lemma 3 are omitteddue to the space limitation. Lemma 1 shows that the EAPcontributing more received power at the information sourcewill receive more reward. Lemma 2 indicates that the EAPsproviding the same received power will get the same amountof reward. Lemma 3 shows that a higher type EAP should begiven more reward. Together with Lemma 1 and Lemma 2, itcan be duduced that a higher type EAP also contributes moreenergy to the information source. We define this feature asmonotonicity. Definition 3: Monotonicity. If θ i ≥ θ j , ∀ i, j ∈ { , . . . , K } and then π i ≥ π j .Based on the above analysis, we can now use the ICcondition to reduce the IR constraints and have the followinglemma. Lemma 4:
With the IC condition, the IR constraints can bereduced as π − q θ ≥ . (19) Proof.
Due to the IC condition, we have π k − q k θ k ≥ π − q θ k . (20)Since we have defined that θ < θ < · · · < θ K , we have π k − q k θ k ≥ π − q θ ≥ . (21)Note that (21) shows that with the IC condition, if the IRcondition of the EAP with type θ holds, the IR condition ofthe other K − types will also hold. So the other K − IRconditions can be bind into the IR condition of the EAP withtype θ .We can also reduce the IC constraints and attain the follow-ing lemma. Lemma 5:
With monotonicity, the IC condition can bereduced as the local downward incentive compatibility (LDIC),given by π i − q i θ i ≥ π i − − q i − θ i , ∀ i ∈ { , . . . , K } , (22)and the local upward incentive compatibility (LUIC), given by π i − q i θ i ≥ π i +1 − q i +1 θ i , ∀ i ∈ { , . . . , K − } , (23) Proof.
There are K ( K − IC constraints in (18), which canbe divided into K ( K − / downward incentive compatibility(DIC), given by π i − q i θ i ≥ π j − q j θ i , ∀ i, j ∈ { , . . . , K } , i > j, (24) and K ( K − / upward incentive compatibility (UIC), givenby π i − q i θ i ≥ π j − q j θ i , ∀ i, j ∈ { , . . . , K } , i < j, (25)Let’s first prove the DIC can be reduced as the LDIC. Byusing the LDIC for three continuous types, θ i − < θ i <θ i +1 , ∀ i ∈ { , . . . , K − } , we have π i +1 − q i +1 θ i +1 ≥ π i − q i θ i +1 , (26) π i − q i θ i ≥ π i − − q i − θ i , ∀ i. (27)By applying the monotonicity, i.e., if θ i > θ j , then π i > π j , ∀ i, j ∈ { , . . . , K } , we have θ i +1 ( π i − π i − ) ≥ θ i ( π i − π i − ) , (28)Combine (27) and (28), we have π i − q i θ i +1 ≥ π i − − q i − θ i +1 . (29)Combine (29) and (26), we have π i +1 − q i +1 θ i +1 ≥ π i − − q i − θ i +1 . (30)So far, we have proved that type θ i +1 will prefer contract item ( q i +1 , π i +1 ) rather than contract item ( q i − , π i − ) . By using(30), it can be extended downward until type θ , and thus allDIC holds. π i +1 − q i +1 θ i +1 ≥ π i − − q i − θ i +1 ≥ . . . ≥ π − q θ , ∀ i. (31)So we conclude that with the monotonicity and the LDIC, theDIC holds. Similarly, we can prove that with the monotonicityand the LUIC, the UIC holds.The LDIC and the LUIC can be combined as shown inLemma 6. Lemma 6:
Since the optimization objective function is anincreasing function of q k and a decreasing function of π k , theabove optimal problem can be further simplified as max ( q m ,π m ) E { U DAP } s.t. π − q θ = 0 ,π k − q k θ k = π k − − q k − θ k , ∀ k ∈ { , . . . , K } ,π K ≥ π K − ≥ · · · ≥ π ,q k ≥ , π k ≥ , θ k ≥ , ∀ k ∈ { , . . . , K } . (32)The proof of Lemma 6 is omitted due to the space limitation.We now solve the optimization problem (32) to attain the opti-mal contract in the subsequent way: a standard method is firstapplied to resolve the relaxed problem without monotonicityand the solution is then verified to satisfy the condition ofthe monotonicity. By iterating the first and second constraintsin (32) and substituting π k , ∀ k ∈ { , . . . , K } into E { U DAP } , TABLE I: System Settings Parameters ValuesEnergy harvesting efficiency η W a m [0.1,1] d m,s [5m,10m] d a,s [15m,25m]Path-loss coefficient α N − mW all π k , ∀ k ∈ { , . . . , K } are removed from the optimizationproblem (32), which becomes max q k N X n =0 N − n X n =0 · · · N − P K − i =0 n i X n K − =0 Φ n ,...,n K × " W log γ K X k =1 n k q k ! − K − X k =1 θ k − K X i = k n i + 1 θ k K X i = k +1 n i ! q k − n K θ K q K ,s.t. q k ≥ , ∀ k ∈ { , . . . , K } . (33)Note that (33) becomes a concave problem. So we can leveragestandard convex optimization tools in [14] to solve it to get q k , and then π k can be calculated iteratively by the first twoconstraints in (33). Moreover, monotonicity is met automati-cally when the type is uniformly distributed [7]. So far, wehave derived the optimal contract ( q k , π k ) , ∀ k ∈ { , . . . , K } ,which can maximize the utility of the DAP and satisfy theconstraints of IR and IC.IV. S IMULATIONS AND D ISCUSSIONS
In this section, we first evaluate the feasibility of theproposed contract, and then demonstrate the performance ofthe proposed incentive mechanism. For the purpose of com-parisons, another two incentive mechanisms are also simulatedin this section. The performance of the optimal contract withcomplete information (i.e., the DAP knows exactly the types ofthe EAPs) is introduced as the upper bound. The other one is alinear incentive mechanism, in which the DAP sets a uniformprice P for unit quality of received energy that is optimizedto maximize the utility of the DAP.The main system parameters are shown in Table I. Since θ = G m,s /a m and γ = ηG a,s /N , the practical ranges of θ and γ can be determined by the parameters shown in Table I. TheDAP’s type θ is uniformly distributed. The unit of achievablethroughput is set as Mbps.To verify the feasibility (i.e., IR and IC) of the proposedscheme under information asymmetry, the utilities of EAPswith type 3, type 6 and type 9 are plotted in Fig. 2 as functionsof all contract items ( q k , π k ) , k ∈ , , . . . , K . It can be seenthat each of the utility achieves its peak value only when itchooses the contract item designed for its corresponding type,which suggests the IC constraint is satisfied. For example,for the type 6 EAP, it achieves the peak value only when Contract item for a certain type EAP U t ili t i e s o f EAP s -0.5-0.4-0.3-0.2-0.100.1 type 3type 6type 9 peak values Fig. 1: Utilities of EAPs with type 3, type 6 and type 9 asfunctions of contract items designed for all kinds of EAPsfrom type 1 to type 10. We set N = 5 and K = 10 . γ S o c i a l W e l f a r e Complete informationAsymmetric informationLinear
Fig. 2: Social welfare as a function of γ . We set N = 2 and K = 5 .it selects the contract item ( q , π ) , which is designed forits type. If the type 6 EAP selects any other contract item ( q k , π k ) , k ∈ , , . . . , K and k = 6 , its utility will be lessthan that when it selects the contract item ( q , π ) . Moreover,when each of above type EAPs (i.e., type 3, type 6 and type 9)chooses the contract item designed for its corresponding type,the utilities are nonnegative. Note that similar phenomenon canbe observed for all other types of EAPs when they select thecontract item designed for their corresponding types, which arenot shown in Fig. 1 for brevity. So the IR condition is satisfied.It can be concluded that utilizing the proposed scheme, EAPswill automatically reveal its type to the DAP after its selection.This means that using the proposed scheme, the DAP cancapture the EAPs’ private information (i.e., its type), and thusovercome the problem of information asymmetry.To evaluate the performance of the proposed scheme withasymmetric information, we compare its corresponding socialwelfare with those of the optimal scheme with completeinformation and another linear scheme with asymmetric in- γ N o r m a li z ed S o c i a l W e l f a r e Asymmetric informationLinear
Fig. 3: Normalized social welfare as a function of γ . We set N = 2 and K = 5 .formation. Fig. 2 plots the curves of the social welfare as afunction of γ . Fig. 3 shows the normalized social welfare asa function of γ , where social welfare of the proposed schemeand linear scheme are normalized by the social welfare of theoptimal scheme with complete information. It can be observedfrom Fig. 2 that the utilities achieved by three of schemes allincrease with γ . This is because with the same P Nm =1 q m , thelarger the value of γ , the larger the achievable throughput R sa (refer to (5)), and thus larger social welfare (refer to (13)).Moreover, it is also shown in Fig. 2 that the performanceof the optimal scheme with complete information providingthe best performance serving as the upper bound, and thethe performance of the linear scheme is the worst. It can beseen in Fig. 3 that the performance of the proposed scheme isgenerally larger that of that of the optimal scheme withcomplete information, and gradually approach to it with theincreasing of γ . This demonstrates that the proposed incentivemechanism can effectively overcome information asymmetryby leveraging contract theory. While the performance of thelinear scheme is generally less than of that of the optimalscheme with complete information. This is because the linearscheme does not utilize the private information (i.e., type) ofthe EAPs, and thus achieves a much lower social welfare.V. C ONCLUSIONS
We developed a contract theory based incentive mechanismfor the energy trading in radio frequency energy harvesting(RFEH) based Internet of Things (IoT) systems. By providingcompatible incentive to the energy access points (EAPs)under information asymmetry, the expected utility of the dataaccess points (DAP) as well as social welfare is maximized.Moreover, the proposed mechanism can approach the perfor-mance of the optimal contract with complete information andsignificantly outperform the linear pricing-based approach.A
CKNOWLEDGMENT
This work was supported in part by ARC grantsFL160100032, DP150104019 and FT120100487. Zhanwei
Hou’s research is also supported by International Postgradu-ate Research Scholarship (IPRS) and Australian PostgraduateAward (APA). R
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