Dynamic Contract Incentives Mechanism for Traffic Offloading in Multi-UAV Networks

Traffic offloading is considered to be a promising technology in the Unmanned Aerial Vehicles(UAVs-) assisted cellular networks. Due to their selfishness property, UAVs may be reluctant to take part in traffic offloading without any incentive. Moreover, considering the dynamic position of UAVs and the dynamic condition of the transmission channel, it is challenging to design a long-term effective incentive mechanism for multi-UAV networks. In this work, the dynamic contract incentive approach is studied to attract UAVs to participate in traffic offloading effectively. The two-stage contract incentive method is introduced under the information symmetric scenario and the information asymmetric scenario. Considering the sufficient conditions and necessary conditions in the contract design, a sequence optimization algorithm is investigated to acquire the maximum expected utility of the base station. The simulation experiment shows that the designed two-stage dynamic contract improves the performance of traffic offloading effectively.


Introduction
Recently, due to their flexible deployment and low cost, Unmanned Aerial Vehicles (UAVs) have been widely used in wireless networks [1,2]. The rapid mobility of the UAVs can effectively increase network capacity and coverage of the Base Station (BS) [3]. In addition, owing to the low deployment cost of the UAVs, the multi-UAV network is considered as a compelling technology for traffic offloading in the traditional cellular networks [4,5].
In the typical wireless cellular networks, when major events or emergent situations occur, the traffic demands will increase rapidly in certain areas. Due to the limited communication coverage and power of the BS, it is difficult for users to obtain a sufficient communication service in the hotspot areas. In this case, considering their flexibility and the low cost, the BS may need the UAVs to offload certain wireless traffic. However, the UAVs may consume certain energy when participating in traffic offloading. Without any incentive, the selfish UAVs may not be willing to offer their help [6,7]. In this work, we will focus on designing a powerful traffic offloading incentive mechanism to address the problem.
Currently, the traffic offloading incentive problem has been investigated in wireless networks [8][9][10][11][12][13][14]. Most research works are performed under the complete network information. However, due to the shadowing and fading effects of the transmission channel and the mobility of the UAVs, it is challenging to obtain the complete network information. Moreover, the UAVs may often belong to different network operators. Due to their selfishness, the UAVs may be reluctant to share their communication information with others. Then, the asymmetric information issue arises between the BS and the UAVs [15][16][17]. Therefore, this paper concentrates on the contract theory-based mechanism to solve the asymmetric information problem in the multi-UAV networks.
Contract theory [18] is an economic concept, which investigates how to design the mutually agreeable contract between the economic entities under the information asymmetric scenario. Currently, contract-based methods are widely applied in many fields [19][20][21][22][23][24][25][26][27][28][29][30][31][32]. However, most works were designed for one-shot incentive. Nevertheless, in certain scenarios, due to the instability of offloading demand, the BS may repeatedly request the UAVs to perform traffic offloading. Under this circumstance, contracts between the two sides are often repeated over time. Moreover, considering the mobility of the UAVs and the dynamic condition of transmission channels, the network environment may change randomly. Therefore, in order to adapt to the dynamic network environment, this paper proposes a long-term contract theory-based traffic offloading incentive mechanism. Our contributions are summarized as follows.
(i) New Solution Technique. As far as we know, this is the first long-term dynamic contract design for traffic offloading in the multi-UAV networks (ii) Feasibility of Contracts. In order to capture the dynamic characteristics of the UAVs in traffic offloading, the dynamic contract mechanisms are designed under both the two information scenarios. Under the symmetric information scenario, the contract only needs to introduce the individually rational (IR) constraint to ensure that the UAVs can achieve the nonnegative utility when participating in traffic offloading. Moreover, under the asymmetric information scenario, the incentive-compatible (IC) constraint is considered to ensure that the UAVs can achieve their maximum utilities when choosing the contract item related to their communication information. In order to obtain the optimal traffic offloading-reward scheme, a sequence optimization method is proposed (iii) Performance Analysis. Simulation results show the effectiveness of the dynamic contract incentive mechanism. By breaking the information asymmetry, the proposed method can increase the BS's long-term utility in traffic offloading The key notations summarized in this paper are shown in Table 1. The rest of this paper is organized as follows. In Section 2, we present the system model and problem formulation. In Section 3 and Section 4, the dynamic contract incentive mechanisms are investigated under both the two information scenarios. Simulation results are given in Section 5. Conclusions and future works are presented in Section 6.

Related Works
In recent years, the incentive problem has been investigated in wireless networks. In [8], Kang and Sun explored the incentive mechanism to stimulate WIFI access points to provide higher quality services for mobile network operators. Zhang et al. proposed a service-based incentive mechanism to facilitate the cooperation of multiple cellular networks [9]. In [10], Hou et al. studied a social-aware incentive mechanism for mobile data offloading. Noreen and Saxena investigated a game-theoretic incentive mechanism for mobile data offloading [11]. In [12], Yao et al. studied a locationaware incentive mechanism for traffic offloading in heterogeneous networks. Mansouri et al. [13] proposed an incentive framework for mobile data offloading with price competition. In [14], Liu et al. designed an offloading incentive mech-anism combined with anchoring effect and loss aversion in the Internet of Things. However, most of the above works were performed under the complete network information scenario. Practically, an asymmetric information problem may exist between the BS and the UAVs. Therefore, an effective mechanism should be adopted to solve the asymmetric information problem in the multi-UAV networks. Different from the above incentive methods, contract theory is an effective mechanism to solve the asymmetry network information issue in many areas, such as energy trading [19,20], spectrum trading [21,22], cooperative communication [23][24][25], Internet of Things [26,27], and deviceto-device communication [28,29]. In addition, contract theory-based incentive mechanism has also been investigated in traffic offloading. In [30], Li et al. proposed an incentive mechanism based on contract theory for delayed traffic offloading in cellular networks. Du et al. designed a contractbased incentive mechanism to investigate the mobile traffic offloading and resource allocation issue in SDWN-based HetUDNs [31]. In [32], Hu et al. formulated a spectrum trading contract for UAV-assisted cellular networks. However, most works designed the contract mechanism for a oneshot static incentive. Nevertheless, in the practical scenarios, due to the dynamic characteristic of offloading demand and network environment, a long-term dynamic contract mechanism should be considered in multi-UAV networks.

System Model and Problem Formulation
In this paper, a typical multi-UAV network is considered, as shown in Figure 1. The network is composed of one BS and N UAVs. Since the traffic sharply increases in the hotspot areas, the BS can employ the UAVs to participate in traffic UAV's private information in stage 1 and stage 2 UAV's reward in stage 1 and stage 2 where c i is the unit cost for i th UAV. Here, we define θ i = c i /hðRT i , DÞ as the private information of the i th UAV, which can describe the ability of traffic offloading of each UAV. When θ i increases, it means that the i th UAV has a higher transmission cost or the poorer condition of a wireless channel. Since the private information θ i is a random variable, we assume that θ i is distributed in a positive interval Θ ∈ ½θ L , θ H with a probability density function f i ðθ i Þ and the corresponding distribution function F i ðθ i Þ.
Since the UAVs may consume the energy when participating in traffic offloading, the UAVs need to go back to their own initial locations to recharge the battery. Assume that the cost E i is consumed by the position movement of UAVs. Then, the total cost of the i th UAV in traffic offloading can be obtained as Thus, the i th UAV's utility U UAV i can be defined as the reward w i received from the BS minus the total cost C i , that is 3.2. Base Station. With the UAVs participation in traffic offloading, the achievable profit of the BS can be defined as where n 0 is the noise power, ρ i > 0 is the profit per transmission capacity. For the convenience of the following analysis, the noise power n 0 is normalized to be 1. Then, by subtracting the UAV's total reward from the achievable profit π, the BS's expected utility U BS can be obtained, which is given by 3.3. Problem Formulation. This work studies the two-stage contract incentive mechanism under the dynamic asymmetric information scenario. Since the UAV's private information is unknown to the BS, the designed contract not only needs to break the information asymmetry, but also should attract the UAVs to perform traffic offloading. Based on the revelation principle [18], in order to reflect the UAV's private information of two stages, the BS needs to design one contract item for each type of UAV at each stage. Here, the two-stage contract is defined as Figure 1: The typical multi-UAV network.

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i and p 2 i are the transmission powers of the i th UAV in stage 1 and stage 2, respectively; w 1 i and w 2 i are the received rewards of the i th UAV in stage 1 and stage 2, respectively.
The timing diagram of the two-stage contract is shown in Figure 2. The whole incentive mechanism is described as follows.
(i) Contract confirmation in stage 0: at the beginning of the contracting stage, only UAVs know their own private information θ 1 i of stage 1. The BS broadcasts a two-stage contract i g to all the potential UAVs. When the UAVs receive the contract, each UAV evaluates and notifies the BS to accept or reject the contract (ii) Traffic offloading in stage 1: the BS informs each UAV of some communication details, such as the serviced hotspot area and allocated channel. Then, the UAVs go to the corresponding serviced area for traffic offloading. When certain UAVs complete the traffic offloading of stage 1, the BS evaluates the UAV's operation through feedback from the hotspot areas. If the traffic is offloaded successfully, the UAVs will get the rewards w 1 i according to the contract. If they fail, the UAVs will not receive any reward (iii) Traffic offloading in stage 2: the second stage of traffic offloading is similar to that of stage 1. After the UAVs complete the traffic offloading work, the BS pays the UAVs the rewards w 2 i according to the contract

Dynamic Contract Incentive
Mechanism under Symmetric Information Scenario In this section, we discuss a two-stage dynamic contract design for traffic offloading under the symmetric information scenario. Here, the BS knows the private information of each UAV precisely. Considering the two-stage contract design, the total expected utility of the BS can be defined as where δ is the discount factor. When δ is greater than 1, it means that the working time of stage 2 is greater than that of stage 1.
Notice that when the i th UAV signs a long-term contract with the BS, it only knows the type of stage 1 θ 1 i . After traffic offloading is realized in stage 1, its private information of stage 2 θ 2 i can be learned by the i th UAV. Thus, the optimal long-term contract is designed by jointly considering the optimal contract with interim contracting (interim contracting describes the process that the BS offers the contract to the UAVs once the UAVs have already learned their private type information.) in stage 1, and the optimal contract with exante contracting (ex-ante contracting shows the process before the UAVs learn their private type information.) in stage 2.
Moreover, considering that the private information of certain UAV in stage 1 may be different from that in stage 2, we use θ 1 i and θ 2 k to indicate the private information in stage 1 and stage 2, respectively.

Contracting Design in Stage 2.
Based on the idea of reverse induction, we first consider the situation of stage 2. The utility of type-θ 2 k UAV in stage 2 is given by whereθ i is the announcement about its private information of the i th UAV in stage 1, p 2 k ðθ i Þ and w 2 k ðθ i Þ are the transmission power and the obtained reward of the i th UAV in stage 2, respectively.
In order to make sure that type-θ 2 k UAV obtains a nonnegative utility by selecting the contract item related with θ 2 k , the contract needs to satisfy the following individually rational (IR) constraint   Wireless Communications and Mobile Computing 4.2. Contracting Design in Stage 1. In stage 1, the i th UAV's utility U 1 UAV i can be written as Considering that the expected continuation utility of stage 2 is in order to make sure that the i th UAV obtains a nonnegative utility by selecting the contract item related with θ 1 i , the contract must satisfy the following IR constraint, 4.3. Optimal Contract Design. In order to achieve the maximum expected utility of the BS in (6), the optimization problem of the two-stage contract design can be defined as follows: Lemma 1. In order to ensure that the BS obtains the maximum expected utility, the utility of each UAV in each stage should be zero, that is, Proof. Since the BS's utility in (6) is decreasing in both w 1 i and w 2 k ðθ i Þ, the BS can acquire its maximum utility by decreasing both w 1 i and w 2 k ðθ i Þ.
From the IR constraint of stage 2 in (8), we can obtain the minimum reward of the i th UAV in stage 2, that is, Similarly, from the IR constraint of stage 1 in (10), the minimum reward of the i th UAV in stage 1 can be obtained as Then, from (13), we have U 2 UAV k ðθ 1 i Þ = 0. Therefore, the UAV's reward (14) can be simplified as This completes the proof. Thus, by bringing (13) into (6), the BS's expected utility U 2 BS in stage 2 is given by Similarly, by combing (15) with (6), we can also obtain the BS's expected utility U 1 BS in stage 1, that is, Then, the BS's expected utility U BS (6) can be written as In order to simplify the following analysis, we defined Thus, the BS's expected utility U BS can be rewritten as Then, the optimization problem (11) can be simplified as At this point, we simplify the expected utility optimization problem of BS in (11) to acquire the maximum utility Yðp 1 i , p 2 k ðθ 1 i ÞÞ. Any local optimal solution (denoted as fp 1 i ,

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Then, the second derivative is further calculated as From (23) and (24), we can find that the local optimal solutions of (21) and (22) are unique and globally optimal. Therefore, the optimal contract design for traffic offloading under the symmetric information scenario can be obtained as

Dynamic Contract Incentive Mechanism under Asymmetric Information Scenario
In the previous section, we investigated the dynamic contract design in the case of information symmetry. However, in practical situations, the UAV's private information may not be known to the BS, which causes the information asymmetric problem. Therefore, in this section, we will discuss the two-stage dynamic contract design in the case of information asymmetry.

Contracting Design in Stage 2.
Based on reverse induction, we first consider the situation of stage 2. In stage 2, in order to ensure that the type-θ 2 k UAV obtains a nonnegative utility by selecting contract ðw 2 k ðθ i Þ, p 2 k ðθ i ÞÞ, the contract needs to meet the IR constraint in (8).
Then, considering that the type-θ 2 k UAV can only obtain its maximum utility when selecting the contract item related with its type, the IC constraint should be satisfied, which can be defined as UAV i can be written as Then, in order to make sure that the i th UAV obtains a nonnegative utility by selecting the contract item related with θ 1 i , the intertemporal IC constraint is defined as Next, considering that the type-θ 2 k UAV's utility Then, the IC constraint in (28) can be simplified as Then, considering the expected continuation utility in stage 2, the i th UAV's intertemporal IR constraint is defined as Therefore, the two-stage contract optimization problem can be given by Wireless Communications and Mobile Computing

Optimal Contract Design.
Since the optimization problem in (31) is nonconvex, it is challenging to obtain a global optimal solution. Therefore, a sequential optimization method is proposed to obtain the optimal dynamic contract design.

Optimal Contract Design in Stage 2.
Based on the idea of reverse induction, we first consider the situation of stage 2. Since the UAV's utility function U 2 UAV k ðθ i Þ satisfies the following Spence-Mirrlees single crossing condition [33], that is we have which means that the type-θ 2 k UAV's utility Thus, the type-θ 2 k UAV's utility U 2 UAV k ðθ i Þ in stage 2 can be written as By combining (34) with (7), the reward of the i th UAV in stage 2 can be obtained, that is, Thus, the BS's expected utility U 2 BS in stage 2 is given by By changing the integration order of (36), the BS's expected utility U 2 BS in stage 2 can be simplified as where

Optimal Contract Design in Stage 1.
Similarly, to the case of stage 2, we can find that the UAV's utility of stage 1 U 1 UAV i satisfies the Spence-Mirrlees single crossing condition (32). Then, we have which means that the UAV's utility of stage 1 U 1 UAV i is decreasing in θ 1 i . Then, we haveU 1 UAV i ðθ i Þj θ 1 i =θ H = min U 1 UAV i = 0. Thus, the UAV's utility of stage 1 U 1 UAV i can be written as Then, by combining (27), (34), and (39), the reward of the i th UAV in stage 1 can be obtained, that is, Thus, the BS's expected utility U 1 BS in stage 1 is given by

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By changing the integration order of (41), the BS's expected utility U 1 BS in stage 1 can be simplified as Thus, the BS's expected utility U BS can be rewritten as Then, the optimization problem (31) can be simplified as Similarly, we can have the optimal transmission power of the i th UAV in stage 1 and stage 2, that is,

Numerical Results and Discussion
In this section, MATLAB simulation experiments are present to verify the proposed incentive mechanism. The experiment environment is composed of one BS and N = 21 UAVs. For simplicity, in our experiments, we assume that the type of UAV in stage 1 is the same as that in stage 2, that is, θ = θ 1 i = θ 2 k . The UAV's type θ is assumed to be uniformly distributed in the interval ½1, 3. The mobile energy consumption E i of the UAV is uniformly distributed in the interval ½4, 8. In addition, the discount factor δ is set to δ = 0:3. The profit per transmission capacity ρ i is defined as ρ i = 15.
First, we evaluated the optimal dynamic contract design for the private information discrimination under the asymmetric information scenario. Figure 3 shows the utilities of UAVs with the three types when choosing all contract items provided by the BS. Since the utility of each UAV is a convex function, each UAV can only acquire the maximum utility when selecting a contract related with its type. Through this form of contract design, the type of UAV can be automatically reflected to the BS. Then, the information asymmetric problem can be solved through the dynamic contract design. Moreover, each UAV can obtain the positive optimal utility. The optimal utility of the type-4 UAV is more than that of other types. The type-12 UAV obtains the lowest utility among the three types of UAVs. As the private information θ increases, the transmission cost of the UAV increases, which leads to the low obtained utility. Figure 4 shows the performance of the UAV's optimal utility with the various discount factors δ. As the private information of each UAV θ increases, its transmission cost increases, resulting in a decrease in the obtained utility. Moreover, while the discount factor δ increases, the time   Wireless Communications and Mobile Computing for traffic offloading increases with the increasing utility of each UAV. Figure 5 describes the relationship between the type of each UAV θ and the corresponding optimal utility U * UAV i . As the type of each UAV increases, the cost of the UAV increases with the low achieved utility U * UAV i . In addition, when the type of UAVs increases to a certain extent, the transmission cost of UAVs is too high to obtain no utility.
Next, the performance is considered with the three different distributions of UAVs' types. In case A, all types of UAVs are uniformly distributed in the interval ½1, 3 with f ðθÞ = 1/2. In case B, the probability of the lower type is greater than that of the higher type with f ðθÞ = ð8 − θÞ/5. In case C, the probability of the higher type is less than that of the lower type with f ðθÞ = θ/9. Figure 6 shows the BS's optimal utility U * BS under the above three different distributions of the types. We can find that the BS's utility U * BS increases with an increase of ρ i in all the three cases. Moreover, as ρ i increases, there are similar increase tendencies of the BS's utility in all the three cases. However, when the amount of ρ i is too small, the UAV may be not willing to participate in traffic offloading, which leads to the zero utility of the BS.
Finally, we study the performance under both the symmetric information and asymmetric information scenarios. Figure 7 shows the BS's optimal utility U * BS with the different numbers of UAVs. As the number of UAVs increases, the BS's optimal utility U * BS increases in the two scenarios. In addition, in the case of symmetric information, since the type     Wireless Communications and Mobile Computing information of each UAV is known by the BS, the BS can better select the UAVs for traffic offloading. Therefore, the BS's optimal utility U * BS under the symmetric information scenario is higher than that in the case of the information asymmetry. Figure 8 presents the BS's optimal utility U * BS with the various equivalent profits ρ i . In the symmetric information scenario, since the BS knows the private information of each UAV, with the increase of ρ i , the BS's optimal utility under the symmetric information scenario is higher than that in the case of asymmetric information. In addition, when the value of ρ i is very small, the UAV may be not willing to perform traffic offloading for the BS, which makes the BS's utility close to zero.

Conclusions and Future Work
In this paper, a dynamic incentive mechanism is proposed in multi-UAV networks. In order to attract UAVs to participate in traffic offloading, a two-stage dynamic contract is introduced. Traffic offloading with the help of UAVs is regarded as the labour market. The BS designs the contract including the transmission powers and rewards of the UAVs. In addition, based on the feature of network information, two information scenarios are studied. Under the asymmetric information scenario, the designed contract needs to meet the IR constraints. As for the asymmetric information scenario, the optimal contract should satisfy both IR and IC constraints to motivate the UAVs to take part in traffic offloading. A sequence optimization algorithm is proposed to achieve the optimal contract design. The experimental results show that the two-stage dynamic contract design can improve the system performance effectively.
This paper investigates a multi-UAVs incentive mechanism for traffic offloading. For the future work, we will consider how to design the incentive mechanism with multiple BSs and multiple UAVs. The BSs may design contracts and compete to attract UAVs to participate in traffic offloading for their own hotspot areas. Moreover, the proposed twostage dynamic contract model will be extended to the multi-stage scenario. In this case, it will be much more challenging to obtain the optimal contract design. Furthermore, a multi-UAV traffic offloading simulator will be considered to make simulation experiments more practical.

Data Availability
No data were used to support this study.

Conflicts of Interest
The authors declare that there is no conflict of interest regarding the publication of this paper.