Quality-Aware Incentive Mechanism for Mobile Crowd Sensing

Mobile crowd sensing (MCS) is a novel sensing paradigm which can sense human-centered daily activities and the surrounding environment.The impact of mobility and selfishness of participants on the data reliability cannot be ignored in most mobile crowd sensing systems. To address this issue, we present a universal systemmodel based on the reverse auction framework and formulate the problem as theMultiple Quality Multiple User Selection (MQMUS) problem.The quality-aware incentive mechanism (QAIM) is proposed to meet the quality requirement of data reliability. We demonstrate that the proposed incentive mechanism achieves the properties of computational efficiency, individual rationality, and truthfulness. And meanwhile, we evaluate the performance and validate the theoretical properties of our incentive mechanism through extensive simulation experiments.

The effect of the aforementioned mobile crowd sensing applications relies heavily on the quantities of participants.However, the ordinary individuals are not willing to share their sensing capabilities unless there are sufficient incentives.Research on incentive mechanism has been widely concerned by investigators, and considerable designed schemes about the incentive mechanism design have been put forward which can be classified into nonmonetary incentives [18][19][20] and monetary incentives [21][22][23][24][25][26][27][28][29].
The key of any crowd sensing system is not only the quantities of participants but also the sensing quality offered by participants.However, most of the existing solutions usually assume that each sensing task (e.g., air quality in a certain region) in a sensing cycle could be performed by a single participant.It is intuitive that the quality of sensing project would be higher if each sensing task was performed by multiple participants.One of the main reasons is that the sensed data cannot always be trusted because participants maybe intentionally (e.g., malicious participants) or unintentionally (e.g., making mistakes) offer the data contrary to the truth.Another reason may come from the recruitment system model itself.A typical MCS consists of two roles: the recruiter who publicizes the sensing tasks and the participants who constitute potential sensing capability selected by the recruiter from many candidates.The interaction between the recruiter and the candidates is modeled as a reverse auction in many existing solutions which can be illustrated by Figure 1.The recruiter always selects participants according to the sensing plans of the candidates.However, changes always go beyond plans.The participants may not be able to complete the task according to their schedule for unexpected incidents (e.g., a selected participant cannot go to the specific locations claimed in his sensing plan).These participants may offer some forged data or do nothing.As a result, the tasks could not be completed in time.
In this paper, we address the issue of quality-aware monetary incentive mechanism design.We design a truthful incentive mechanism satisfying the properties of computational efficiency, individual rationality, and truthfulness with low approximation ratio.
The remainder of this paper is organized as follows.In Section 2, we review the related work.In Section 3, we describe the system model and formulate the MQMUS problem.Thereafter, in Section 4 we propose the incentive mechanism, named QAIM, which consists of two phases, winner selection and payment determination, and analyze the properties of QAIM.Section 5 presents the experimental results.Finally, we draw the conclusion and discuss some possible future directions in Section 6.
Stackelberg game is a game where one leader player has the dominant influence over the other players [46].Duan et al. [30] make use of the Stackelberg game to design a threshold revenue model for service providers.The system and the users interact through a two-stage process similar to that of Stackelberg game.The system announces the total reward and the threshold number of required participants.Each participant decides whether to accept the task or not.Yang et al. [31] also model the proposed platformcentric incentive mechanism as a Stackelberg game, prove that this Stackelberg game has a unique equilibrium, and design an efficient mechanism for computing it.The above two Stackelberg game solutions have theoretical guarantees.However, the premise of this kind of method is that the costs of all users or their probability distributions are assumed to be known, which limits the applicability of Stackelberg gamebased mechanisms because participants may keep their costs private in the real world.
An auction-based mechanism is originally the process of buying and selling goods by negotiating the monetary prices [47].A kind of auction, called reverse auction, is adopted to model the negotiation process in crowd sensing, which is shown in Figure 1. Lee and Hoh [32] firstly design a reverse auction-based dynamic price incentive mechanism with virtual participation credit with the objective of minimizing and stabilizing the platform cost while maintaining the participation level.Yang et al. [31] consider two system models for smartphone crowd sensing system: the platformcentric model with the solution based on the Stackelberg game and user-centric model with the solution based on the reverse auction.Feng et al. [33] formulate the winning bids determination problem and present a truthful auction for location-aware collaborative sensing.Zhang et al. [34] focus on the user-centric model and study three methods which involve cooperation and competition among the services.Xu et al. [35,36] investigate truthful incentive mechanisms for time window dependent tasks with the strong requirement of data integrity and propose two incentive mechanisms for the single time window case and the multiple window case, respectively.Subramanian et al. [37] consider offline and online incentive mechanisms using the same bidding framework with MSensing Auction proposed in [31].Zhao et al. [38] investigate the incentive mechanisms in the online setting based on an offline budget feasible mechanism [39], which provides a starting point for the online mechanism.Jin et al. [40] pay attention to the quality of the mobile crowd sensing systems and incorporate a metric named QoI  (Quality of Information) into the incentive mechanisms.SRC and MRC mechanisms with the criterion of the combinatorial QoI and price are proposed.However, the authors fail to consider the truthfulness of the MRC mechanism.The aforementioned solutions assume that each measurement of sensing task can be represented by a single sensor reading.Several solutions are proposed to ensure the quality of crowd sensing data.Tanas and Herrera-Joancomartí [48] achieve the first work, which focuses on how to validate sensing data, but the premise of their work is that there are multiple users to submit multiple sensing readings on each task.Kazemi et al. [49] assume each worker has a reputation score, and assign enough number of workers to each spatial task such that workers' aggregate reputation can satisfy the confidence of the task.However, they focus on self-incentivized spatial crowdsourcing, in which people perform the tasks voluntarily without any reward.Zhang et al. [41] propose a task management framework to match workers to the merged query and sensing tasks efficiently.In their model, each task can be assigned to multiple workers, and each worker can be assigned to at most one task, although each worker may have the preference for multiple tasks.Xu et al. [42] design the incentive mechanism, which considers the issue of stimulating the biased requesters in the competing crowdsourcing market.Xiong et al. [43] consider the k-depth coverage as an MCS data collection constraint, but every subtask is assigned to the same value of .Wang et al. [44] present a detailed quality-aware mobile crowdsourced sensing framework, composed of three MCS components: crowd, crowdsourcer, and crowdsourcing platform.The crowdsourcer is a new role who assesses the posted contributions' quality.He et al. [45] propose a recruitment strategy in vehicle-based crowdsourcing through taking full advantage of predictable mobility patterns of vehicles, which bring a new insight to improve the quality of crowd sensing system.However, the behaviors of human are affected by many factors.It is far more difficult to predict the mobility patterns of human beings than those of vehicles.
In this paper, we try to enhance the quality-aware incentive mechanism from two main dimensions: the reputation of participants and the design of task.

Problem Statement
Different from most crowd sensing systems, the objective of this paper is designing the truthful incentive mechanism with maximum social efficiency and high sensing quality.To achieve this objective, the recruiter needs to select participants who can match the diverse requirements of the crowd sensing application with minimum social cost.Before demonstrating the rigorous problem definition, we would like to present a motivating example to make the problem better understood.

A Participant Recruitment Example in Air
Quality Monitoring.We take the urban air quality monitoring MCS task as an example.As shown in Figure 2, the MCS recruiter wants to collect the state of the air in three regions (denoted as  = {, , }).Nine candidates ({V 1 , V 2 , . . ., V 9 }) are interested in performing the task and reporting their sensing plans, which include what they can do with the corresponding bid price.The industrial structures vary greatly in different regions.The regions with more plants, which can discharge waste gas, need more participants to monitor.For example, the recruiter wants 5 participants to monitor region  and only 3 to monitor region  because there are more chemical plants in region .We use squares to represent the regions, and the number above each square denotes its requirement.To the perspective of the candidates, people may not just stay in a certain region in one sensing cycle and can fulfill multiple sensing tasks in different regions.We use disks to represent the candidates, and the number above each disk denotes its corresponding bid price, and the set of regions below each disk denotes the regions that he can monitor.
In this example, the mobile crowd sensing system has some requirements: (1) Every subtask should be assigned to enough participants so that their aggregate sensing results can ensure the sensing quality.( 2) Every subtask has different sensing requirement.The different number of participants should be recruited to satisfy different sensing requirements with minimum costs.(3) Every participant has different ability in terms of the task completion and should be assigned to the different number of subtasks based on his particular ability.

System Model and Problem Formulation.
We present the rigorous definition and formulation of the MQMUS problem.In this problem, the recruiter can divide the task into multiple subtasks with different quality factors and the participants can be assigned to multiple subtasks in one sensing cycle.
Considering  candidates,  = {V 1 , V 2 , . . ., V  , . . ., V  } are interested in performing the sensing task.Each candidate is only used to represent that V  can fulfill the subtask   ) and  V  is bid price that candidate V  wants to charge for performing  V  .
We assume that the candidate V  has a reputation score  V  , which states the probability that the candidate performs a task correctly.The recruiter is responsible for maintaining and updating the reputation score of every candidate.The value of  V  is set to 1 initially and updated by We utilize a voting mechanism to set the value of .This intuition is based on the idea of the wisdom of crowds [50] that the majority of the participants are trusted.The recruiter aggregates the different sensing results to get the reliable result at the end of the sensing cycle.The setting way of  is inspired by [44]. is set to "−1" in two cases: (1) the candidate cannot perform the subtask as the claimed sensing plan; (2) the sensing result of the same subtask is contrary to more than half of participants' results; otherwise,  is "0."If  V  < 0, V  will not be selected until the recruiter resets  V  to 1 after a period of time (e.g., 10 sensing cycles).
Assume that the number of candidates is sufficient to fulfill the sensing task  with its quality constraints ℎ().This assumption is reasonable for mobile crowd sensing systems as made in [31,33,35].The selected participant   is placed into the list  = { 1 ,  2 , . . .,  −1 } according to the order.  is the ID of the candidate and its subscript  denotes that   is the th selected participant.The recruiter has to calculate the payment    for each participant as the incentive.The utility of participant can be calculated by (2), in which    is the real cost of the participant   and only known by itself.   is not less than    due to the selfishness and rationality of participants (if the reputation score of   is set to a value less than 0 in this sensing cycle, the utility of   will be 0 in the next sensing cycle because he will not be selected). ( The utility of the recruiter is calculated by (3).(ℎ()) is the value to the recruiter when it has collected enough data to satisfy the quality constraints ℎ() of the sensing task .
The social efficiency of the sensing task  (with the quality constraints ℎ()) is calculated by (4).Although the real cost    is only known by participant   , we will prove that claiming a different cost    cannot help to increase the utility of participant   in our designed mechanisms.So we use    when we attempt to maximize social efficiency in the mechanisms designed below.The objective of maximizing the social efficiency is equivalent to the objective of minimizing the social cost.
We design a truthful incentive mechanism, QAIM, to select appropriate participants to satisfy the objective of this paper, and to eliminate the fear of market manipulation (the participants cannot improve their utility by submitting a bid price different from its real cost).
We cannot find the optimal solution in polynomial time for the MQMUS problem presented in ( 5) and ( 6) because this problem is NP-hard.The proof is in Appendix.
Our objective is to design the incentive mechanisms satisfying the following four desirable properties to solve MQMUS problem: (i) Computational Efficiency.A mechanism is computationally efficient if both the winner selection function and payment decision function can be computed in polynomial time.(ii) Individual Rationality.Each participant will have a nonnegative utility upon performing the sensing task.(iii) Truthfulness.A mechanism is truthful if no participant can improve its utility by submitting a bid price different from its real cost, no matter what others submit.In other words, reporting the real cost is a dominant strategy for all participants.(iv) Social Optimization.The objective function is maximizing the social efficiency.We attempt to find optimal solution or approximation algorithm with low approximation ratio when there is no optimal solution computed in polynomial time.

Mechanism Design and Analysis
4.1.Mechanism Design.We attempt to find an approximation algorithm following a greedy approach which can be solved in polynomial time because the MQMUS problem is NPhard problem.The winner selection algorithm QAIM() is illustrated in Algorithm 1 and the payment algorithm QAIM() is illustrated in Algorithm 2.
In Algorithm 1,  is the ID of candidates,  is the number of selection round, and   is the set of remaining subtasks excluding those in the sensing plans of the selected participants before the previous  − 1 rounds.The effective sensing units of  in the th round are denoted by   (  ) which can be calculated by (7), the effective average sensing weight of candidate  in the th round is denoted by   () which is calculated in Line (3) of Algorithm 1.
The main idea of greedy approach is to select candidate with least effective average sensing weight, so   () of all remaining candidates are sorted in nondecreasing order in Line (4) of Algorithm 1, and arg(  ()) is the ID of the th selected participant in the th selection round.
The trick of QAIM() lies in the use of min ℎ  which denotes the number of participants that can be selected in the th round.The nondecreasing sorting of   () implies that ( 8) is true.
Equation ( 9) is true; otherwise the first selected participant in the ( + 1)th round will be selected in the th round.
The calculation method of  +1 in Line (10) of Algorithm 1 implies that | +1 | cannot be bigger than |  |, so (10) is true which implies the participant is selected in the nondecreasing order of the effective average sensing weight: Let   ,  +1 , . . .,  +min ℎ  −1 denote the IDs of the selected participants in the th selection round; the set of remaining subtasks would possibly be changed only at the end of the th selection round, so (11) is true.
In Algorithm 2,  is the ID of candidates with the same role as  in QAIM(),  is the number of payment determination round, and   is the set of remaining subtasks excluding those in the sensing plans of the selected participants before the previous  − 1 rounds.The effective sensing units of  in the th round are denoted by    (  ) with the same calculation method used in (7).The effective average sensing weight of candidate  in the th round is denoted by Γ  () which is calculated in Line (5) of Algorithm 2.
To compute the payment for each   in the winner list , we consider the set of candidates  − {  } and reselect appropriate participants into the list    with the same method used in QAIM() (the superscript   of    is used to identify that   is not considered as a candidate).Let  . (13)

A Walk-Through Example.
To better understand the algorithm, we use the example in Figure 2 to illustrate how the QAIM works.
With regard to the aforementioned example, the crowd sensing task  = {, , } is divided into 3 subtasks: ℎ() is set to 3, ℎ() is set to 4, and ℎ() is set to 5.There are 9 candidates  = {V 1 , V 2 , . . ., V 9 } who want to participate in the task and report their sensing plan: the bid price of V  is shown above it, and the subtask that V  can fulfill is given below it in Figure 2. Take V 3 , for example,  V 3 = {, }, which can also be represented as  V 3 = { V 3 ,  V 3 }, and  V 3 = 1.The effective sensing units of V 3 in the first round are denoted by  V 3 ( 1 ) which is calculated by (7) (i.e., |{, , } ∩ {, }| = 2), and the effective average sensing weight of V 3 in the first round is denoted by  V 3 (1) which is calculated in Line (3) of Algorithm 1 (i.e.,  V 3 / V 3 ( 1 ) = 1/2).
We first assume that all participants are trustworthy and can fulfill the sensing units as they had claimed in their sensing plan.
If V 3 is a malicious participant, he lies in the results of all sensing units; the reputation of V 3 is 0 calculated by (1) which means he will not be selected in the next sensing recruitment cycle.
Owning to the limitation of the space and the similarity of the algorithm process, we only give the payment example Table 6: Γ  () in the third payment determination round considering V 3 .

Properties of QAIM.
In this section, we analyze the properties of QAIM theoretically to show that QAIM is computationally efficient, individually rational, and truthful.The approximation is also discussed in the end.We use  to denote the number of candidates,  to denote the number of subtasks, Ω() to denote all the sensing units, and Ω(    ) to denote the effective sensing units of the selected participants  = { 1 ,  2 , . . .,   }, and for ease of analysis they can be calculated by (1)  Is Computationally Efficient.We analyze QAIM() and QAIM(), respectively, where QAIM takes ( 3 * ) in the worst case.
The nested for-loop (Lines ( 8)-( 11)) of QAIM() will be executed  * |   | * min ℎ  times.The maximal value of  is Ω() which is less than  obviously in the worst case when the effective sensing unit of every candidate has only one subtask.|   | is less than  and min ℎ  is far less than  obviously, so QAIM() takes ( 2 * ) in the worst case.QAIM() takes ( 3 * ) in the worst case because there are similar processes in both QAIM() (Lines (2)-( 11)) and QAIM() (Lines ( 4)-( 14)), which will be executed || times less than .
(2)  Is Individually Rational.When considering the set of candidates −{  }, let     be the replacement of participant   which appears in the th place in the selected list 16) is true according to the main idea of winner selection.

𝑥
will not be selected in the th place if   is considered, so (17) is true.
Equation ( 19) is true according to the main idea of payment calculation in Line (9) of QAIM().
Equation (20) shows the fact that   will not be selected before the previous  participants ( (4) The Approximation Factor to Optimal Solution Is ln(Ω()) + 1.Let OPT denote the minimal social cost computed by optimal solution, Ω(    ) denote the effective sensing units of the selected participants  = { 1 ,  2 , . . .,   } calculated by (15), and cost( +1 ) denote the social cost of the ( + 1)th selected participant  +1 .
Because the participant is selected in the nondecreasing order of the effective average sensing weight according to QAIM() and the average cost of the rest uncovered sensing units is not greater than OPT/(Ω() − Ω(    )), ( 21) is true.
Hence the total cost of QAIM can be calculated by

Performance Evaluation
5.1.Before the Simulation Setup.Because there is no real data set which is consistent with the proposed system model, we have to mine the ways of human mobility from Gowalla [52] and Brightkite [53], which come from the location-based social networking website where users share their locations by checking-in.The details of the data sets are listed in Table 7.
We consider the variation law of user's mobile preferences because the sensing task is dependent on location in most crowd sensing systems.Observing a user's visiting history can help discover the user's abilities to fulfill the subtasks in different locations.
We divide the region  into  *  square blocks and let (, ) ∈  denote the block in which ,  ∈ {1, 2 . . ., } represents horizontal and vertical locations, respectively.Let   (, (, )) denote the number of checking-ins of user  during the time period  ∈ [ 1 ,  2 ] in block (, ).If   (, (, )) is greater than zero, (, ) is called the reachable region of user  during the time period .
The reachable regions of user  can be viewed as the subtasks in different locations that the user can fulfill.Let ℎ(, ) denote the number of reachable regions which can be The number of reachable regions With different partition granularity in different data set, more than 95% of the users' number of reachable regions is smaller than 1.25% of the number of region blocks; the complementary cumulative distribution of ℎ(, ) follows the same power-law distribution formulated by (24), which can be seen in Figures 3 and 4, respectively.

𝑝 (𝑋
The phenomenon of power-law distribution is consistent with our life experience: the activity scope of most people has a limited range in several specific regions in their daily life.The above-mentioned result tells us how to set the number of subtasks that the user can fulfill.

Performance Evaluation.
In order to evaluate QAIM, we first introduce two baseline algorithms with the similar ideas of using redundancy.
(i) max() is derived from the K-depth coverage objective solution proposed in [43].No matter how different the sensing quality factor of each subtask is,  is set to the maximal value of these quality factors.
No matter how many subtasks one participant can do, he is only assigned with one subtask at a time.So, the participant is selected in the nondecreasing order of the bid price.
The performance metrics include the social cost, the number of winners, the running time, and the truthfulness, and the importance of reputation score is also checked up.
Simulation parameters are shown in Table 8.Each measurement is averaged over 100 instances.
(1) Impact of ||.Figures 5-7 show the performance of QAIM() with different candidates when the number of sensing subtasks is set to 100.As shown in Figures 5 and 6, the social cost and the number of winners of QAIM() are both less than those of Greedy(1) or max().The variation does not follow the rule of decreasing with increment of the  number of candidates but is within a certain range.The reason is ℎ(  ) and  V  which are generated randomly.QAIM() has superiority in achieving high quality crowd sensing with minimum social cost.The running time of QAIM() is larger than Greedy(1) but less than max() as shown in Figure 7.
The variation trend of the running time is consistent with  the property of theoretical analysis which increases with the increasing number of candidates.
(2) Impact of ||.Figures 8-10 show the performance with a fixed number of 1400 candidates when the number of sensing subtasks varies from 100 to 140 with increment of 10.As shown in Figures 8 and 9, both the social cost and the number of winners of QAIM() increase with the increment of || and are less than other algorithms.The running time of QAIM() is larger than Greedy(1) but less than max() and increases with || as shown in Figure 10, which is consistent with the property of theoretical analysis.
(3) Truthfulness.We verified the truthfulness of QAIM with different candidates when the number of subtasks is set to 100.We randomly selected the 78th participant and changed the bid price  78 of the 78th participant.When  78 >  78 , the 78th participant would not be selected.The running time of QAIM() is recorded in Figure 11  candidates except when the number of candidates is 1300, which is a reasonable phenomenon since the running time of QAIM() is related to not only the number of candidates but also the number of winners.
(4) The Effect of Reputation Value.Finally, we verified the importance of the calculation of reputation value.We first set the 78th participant as the malicious user and offer the contrary sensing result to correct ones of all subtasks intentionally; we find that it would not be selected after the second test.Then we reset the reputation score to 1 and let the 78th participant be selected but the 78th participant does not fulfill one of the subtasks; we find that it would be selected after the second test and would not be selected after the third test.

Conclusion
In this paper, we address the fundamental research issue: how can we achieve high quality crowd sensing with the minimum social cost?To answer this question, we study different conditions of recruiter and candidates in crowd sensing system.Based on the findings, we formulate the sensing quality assurance problem as an optimization problem (MQMUS) and prove it to be NP-hard.We design a polynomial-time greedy approximation algorithm QAIM which consists of two phases: QAIM() selects appropriate participants to satisfy the objective of this research which approximates the optimal solution with the times of ln(Ω()) + 1 and QAIM() eliminates the fear of market manipulation.Through rigorous theoretical analysis, we demonstrate the proposed mechanisms with the properties of high computation efficiency, individual rationality, and truthfulness and then evaluate our algorithm using synthetic data with the features of real data sets.Evaluations show that our algorithms outperform existing approaches.In the future work, we will explore the quality-aware incentive mechanisms in more complex scenarios, for example, how to prevent cocheating using the

Figure 1 :
Figure 1: A typical mobile crowd sensing system as a reverse auction framework.

Figure 2 :
Figure 2: A motivating example with diversity requirements.

Figure 5 :Figure 6 :
Figure 5: The social cost with different candidates.

Figure 7 :Figure 8 :
Figure 7: The running time with different candidates.

Figure 9 :Figure 10 :
Figure 9: The number of winners with different number of sensing subtasks.

Figure 11 :
Figure 11: The running time of QAIM() with different candidates.

Table 1 :
() in the first selection round.

Table 2 :
() in the second selection round.

Table 3 :
() in the third selection round.

Table 4 :
Γ  () in the first payment determination round considering V 3 .

Table 5 :
Γ  () in the second payment determination round considering V 3 .
3)  Is Truthful.According to Myerson's Theorem [51], an auction is truthful if and only if the selection rule is monotone and each winner is paid the critical value   ; if a participant wins the auction by bidding   , he also wins by bidding    <   but loses by bidding    >   .The monotonicity of the selection rule is obvious: if   bids a smaller     that means     /   (  (−1) ) ≤    /   (  (−1) ) is true if    is greater than    .
But if the previous  participants are selected, there is no reason to select   because the previous selected participants can satisfy different sensing requirements.

Table 7 :
Facts about studied traces.