Truthful Mechanism for Task Assignment in Crowdsourcing with Social Network

Macrotasks like document writing, product design, or web development, require expert skills and the collective contributions of the crowds. In fact, there are few studies give close attention to the workers with social network in crowdsourcing. Social networks provide an available platform for cooperation among social workers. In this paper, we discuss the complex task assignment in crowdsourcing where the workers are in a social network. A Truthful Mechanism for the task assignment in Crowdsourcing with Social Network (TMC-SN) is proposed to solve the challenges in this scenario. The problem is modeled as an auction, where the requesters are buyers, workers are sellers, and the crowdsourcing platform serves as an auctioneer. In order to find out the most appropriate team, TMC-SN measures Worker Fitness of the worker for the team from both Marginal Contribution and Team Cohesion. We demonstrate that TMC-SN has fine economic properties such as truthfulness, individual rationality, and budget balance. The evaluation results show that TMC-SN is advantageous in terms of Social Welfare and favorable for the workers.


Introduction
Crowdsourcing, coined by Jeff Howe in 2006, is defined as the method of outsourcing a specific task to an set of uncertain people instead of assigning it to designated employees. From then on, crowdsourcing is prevalent in many fields. In fact, the technique of crowdsourcing can be traced back to 1884 when Oxford English Dictionary depended on a crowd to catalog words [1]. Amazon Mechanical Turk is a functional crowdsourcing platform where employers release tasks such as translation and labelling etc and Internet workers like to complete tasks with small rewards. Despite micro payments, part-time or full-time crowds are willing to take different types of tasks which not only decreases overall expense of the requester but also helps to generate high-quality work.
It is worth noting that there are few studies that give close attention to the workers with social network in crowdsourcing. Conversely, the scientific collaboration network has been considered as a representative social network in previous studies, in which teamwork is an important issue in scientific and technological activities [2]. Obviously, some research projects are too complex to be performed by a single scientist. Therefore, scientific projects are necessarily conducted with the collaboration of many scientists who tend to form or have builded up communities in accordance with their research topics and interests. Social networks provide an available platform for cooperation among social workers. In crowdsourcing, TopCoder is a representative crowdsourcing marketplace for software development which needs the cooperation of a set of workers to generate the project. Actually, once the social network of the workers is introduced into crowdsourcing, it is triple-win for the workers, task requesters and the the platform. The workers would rather collaborate with those who are familiar with than those who need to be further run-in. Then, the task would be completed more outstandingly and efficiently. Task requesters are certainly glad to receive the finished task with higher-quality. Furthermore, the platform may hire less workers and then cut costs. In this paper, we discuss the complex task assignment in crowdsourcing where the workers are connected. The problem is modeled as an auction, where the requesters are buyers, workers are sellers, and the crowdsourcing platform serves as an auctioneer. After the requester posts the task and the connected workers submit skills, the platform will make the assignment. In this scenario, there are several unsolved challenges. First of all, it has been proved that the complexity of task assignment in social networks remains NP-hard [3]. Thus, presenting an efficient mechanism is the most important issue. After that, the workers in social networks are connected with complex relationship. In that way, the mechanism should figure out the relations of the connected workers and then find out a suitable team. Last but not least, the self-serving workers may attempt to misreport their ask to gain a higher utility. Therefore, the mechanism has to be truthful.
A Truthful Mechanism for the task assignment in Crowdsourcing with Social Network (TMC-SN) is proposed to solve the challenges mentioned above. In TMC-SN, an efficient assignment within polynomial time complexity is proposed. In order to find out the most appropriate team, TMC-SN measures Worker Fitness of the worker for the team from both Marginal Contribution and Team Cohesion. Conventional solution ignored the self-centred players who may misreport their value in order to gain higher utility. However, auction is introduced into TMC-SN as a valid method to forbid the players from lying. TMC-SN satisfies all the properties of auction, truthfulness, individual rationality, and budget balance.
The remainder of this paper is structured as follows. The detailed system model and some definitions are described in Section 2. We present the design of TMC-SN in detail in Section 3 and then analyse related properties, specifically the truthfulness. Our simulation results are presented in Section 4, followed by conclusions in Section 5.

System Model
Social Networks: A social network, SN = A, E, D is an undirected graph, where A = {a1, a2, . . . , am} is the set of workers. ∀ (ai, aj) ∈ E indicates that there is a direct social interaction between ai and aj. Each pair of workers, (ai, aj) ∈ E is associated with a cost d (ai, aj) ∈ D incurred by the necessary communication and d (ai, aj) = d (aj, ai). In other words, d (ai, aj) ∈ D is the value of edge for (ai, aj) ∈ E.
Requester: The requester posts her task R with bid b to the platform. b is the requester's claimed value if the task is completed andb is the truthful value. We assume that there are τ types skills S = {s1, s2, . . . , sτ } the requesters need. SR = {s 1 r , s 2 r , . . . , s τ r } is a τ -dimension vector, where s k r = {0, 1} means that k-th skill is required or not in R. We assume that there is an uncovered skill vector S R as the members are added into the team and S R is the same as SR at the beginning of process.
Worker: Each worker ai ∈ A submits a tuple Ci = {< s k i , c k i > k=1,2,...,τ } to the platform. Among Ci, s k i = {0, 1} denotes whether ai holds the k-th skill or not and c k i is the reward that ai expects to be paid by contributing s k . c k i is not necessary equal toc k i which is the true cost of performing the s k . C = {C1, C2, . . . , Cm} is the bid vector of all the workers. N ei (ai) is the set of agents who have the direct connection with ai.
The worker may contribute one or several skills to the task. Therefore, we import overall cost oCi to deal with the gathering skills. H = {h1, h2, . . . , hτ } represents the weight vector of S, where h k means the workload of the skill s k . If ai has the skills that is required in S R , the overall cost of ai can be calculated as follows.
Platform: After gathering information about requesters and workers, the platform produces the outcome of the auction, including the chosen team members T ⊆ A and the payment vector P = {p1, p2, . . . , pm} of the workers in T .
Therefore, the utility of the requester is the difference between the value and the payment: Similarly, the utility of winning worker ai ∈ T is the reward from the auctioneer minus the cost of supplying the skills: Here,õ Ci is the true overall cost corresponding to oCi.

Definition of Concepts
In this section, we introduce several economic properties we are desirable to achieve and some concepts we will use. Definition 1. (Truthfulness). An auction is truthful shows that neither buyers nor sellers can gain a higher utility by deviating from their true value or cost. In our auction, it implies for ∀ai ∈ A, if oCi =õ Ci, Ui is maximized; for R, if b =b, UR is maximized.
Truthfulness is the most crucial property in auction theory. Since exposing true bid or ask procures the highest utility, no rational buyer or seller would cheat any more. As a result, the trade can be free from market manipulation. In addition, irrespective of other's behavior, players would simply apply their truth-telling strategy so that the system would reach an equilibrium. Myerson theorem is the most common theory used in auction which is shown as follows.

Theorem 1. (Myerson theorem) An auction mechanism is truthful if and only if [4]:
• Monotone allocation: If ai is allocated successfully by bidding c k i , he can also win by bidding c k ≤ c k . • Critical value: If ai asks higher than the critical value, he will not win the auction.
Definition 2. (Individual Rationality). A winning seller is paid more than his cost and the winning buyer is charged less than her budget. In other words, if the trade is successful, for ∀ai ∈ T , pi ≥ oCi; for R, a i ∈T pi ≤ b.
Definition 3. (Budget Balance). Budget balance means that the budget from the requester is more than the total payment to the workers, i.e., b − a i ∈T pi ≥ 0.
Definition 4. (Social Welfare). Social Welfare is calculated as the aggregate utility of all the winning buyers, sellers and the auctioneer. It is also defined as the difference between the sum of winning buyers' value and the sum of winning sellers' costs.

Design Details
Many factors will influence the performance of a team. The requester prefers the workers who can make more contributions to the team. It is mentioned in Ref. [5] that group cohesion was positively related to overall performance. Therefore, considering both contribution and cohesion, we give the definitions as follows. Here, α ∈ [0, 1] is a tune parameter between Marginal Contribution and Team Cohesion and nor(·) is the normalization function.
The TMC-SN mechanism is shown in Algorithm 1. At the beginning of the mechanism, we search for the neighbours of the teammates and add them into N eis. In allocation rule, the worker with the smallest cost per fitness is selected as the candidate, i.e., the lowest oC i f itness(a i ) . It's worth mentioning that the candidate workers are connected with each other. Only the neighbors of ai ∈ T will be added into the team. In other words, the winning workers form a connected subgraph at the end of the process. The payment rule follows the Myerson Theorem in order to make sure that the selected worker is paid the highest cost he can report or else he will not DMCIT2019 IOP Conf. Series: Journal of Physics: Conf. Series 1284 (2019) 012038 IOP Publishing doi:10.1088/1742-6596/1284/1/012038 4 be selected. We rebuild the team without the participation of ai. It select aj from {N eis \ T } with the smallest cost per fitness and aj still has the connection with the existing workers. Therefore, In the case that , aj will be selected instead of ai.
Repeat selecting aj until the budget is run out or the skills are covered. Throughout the process, the largest value { oC j f itness(a j ) * f itness (ai) , pi} is set as the critical value of ai. Moreover, if the payment for ai is less than remaining budget, ai will be the winner. During the process, ∆i and Γi are updated once a new worker is added into the team. In the end of the process, the trade is a success in the case that the skill requirements of R are covered.

Analysis of Desirable Properties
Having given the detailed design of TMC-SN, we now prove that TMC-SN achieves truthfulness, individual rationality, and budget balance.

Theorem 2. TMC-SN achieves truthfulness.
Proof: The truthfulness of the requester is obvious. There are two possible reasons why R can not be allocated. One is that the skills of R cannot be covered by the remaining workers, and the other is that the budget is limited. If it's the first reason, the requester can not be assigned anyway. If a requester with a limited budget wants to be successfully allocated, the requester must raise the bid until it is higher than the asks of the DMCIT2019 IOP Conf. Series: Journal of Physics: Conf. Series 1284 (2019) 012038 IOP Publishing doi:10.1088/1742-6596/1284/1/012038 5 team. However, it would result in a negative benefit for the requester. Therefore, the requester will not lie about his bid.
For the workers, it is obvious that TMC-SN has a monotone allocation. If ai is selected by bidding c k i , he can also be selected by bidding c k i ≤ c k i with a smaller oC i f itness(a i ) . The payment to ai is decided by selecting a team without ai's participation. aj is selected from the set N eis\{K ai} with the minimum . In the case that , aj will be selected instead of ai. The payment to ai is temporarily equal to p i = oC j f itness(a j ) * f itness (ai). Here, p i isn't the highest price which ai can report because his competitors in N eis\{K ∪ ai} haven't been considered entirely and the skill requirements of ai haven't been covered. Therefore, the process of iteration continues until all the skills are covered or the budget is exhausted. Finally, the payment is the critical value, i.e., pi = max{ Because of critical value, if ai asks higher than pi, ai will be placed after the last selected worker, then ai will not be selected as the winner. From above, the critical value has been proved. Adhering to Theorem 1, the truthfulness of workers is proved.
Proof: For the requester, b ≥ pi is checked every time before including a new teammate and the budget is updated after a successful trade. In other words, remaining budget is always higher than the payment to the new joined workers. Thus, In general, the individual rationality of TMC-SN is achieved.
Proof: According to the payment rule, the remaining budget is checked whether enough for the payment of the new joined workers. Hence, we have b − a i ∈T pi ≥ 0. The budget balance of TMC-SN achieves.

Performance Evaluation
In this section, we simulate a crowdsourcing platform where workers are in a social network. In the experiment, the truthfulness of the TMC-SN is verified. The TMC-SN mechanism is compared with the complex task mechanism design without social network structure, non-SN, in terms of number of transactions, utility, and social welfare.

Simulation Settings
The number of workers m varies from 10 to 100 with a default value of 50. The bid of requester is randomly distributing over (0.5, 6.5]. The ask of workers for a single skill is randomly selected in the interval (0, 1]. If (ai, aj) ∈ E, the distance between ai and aj, d (ai, aj), is varied from 2 to 12. We assume that the requester demands 6 kinds of skills at most. The tune parameter α is randomly selected in the interval (0, 1], and the default value is 0.5. Some indicated datum in the figures is the average result of 1000 independent instances in each setting. In each instance, there is only one requester post one task.

Truthfulness
In this section, the truthfulness of players in TMC-SN mechanism is analyzed. One winner and one loser are randomly selected, and then their utilities are examined when they ask or bid different value. As shown in Figure  1(a), a randomly selected winning requester bids truthfully with b =b = 4.57 and achieves utility 2.13. When the winning requester attempts to decrease his bid to gain a higher utility, he would fail and gain no utility. Similarly, the loser case in Figure 1(a) indicates that when a losing requester raises his ask to win the auction, he would gain a negative utility. The truthfulness of workers in Figure 1(b) can be explained in the same way.

Comparison of TMC-SN and non-SN.
In this section, non-SN is introduced to compare with TMC-SN. In the non-SN mechanism, the social relations among workers are neglected. In that case, the Worker Fitness is only related to Marginal Contribution, i.e., α = 1. From Figure 2(a), it can be observed that with the increase of workers, the number of transactions of non-SN is always higher than that of TMC-SN. This is because that TMC-SN considers the Team Cohesion of workers. The more stringent the trading are, the lower the transaction rate will be. Figure 2(b) indicates that the utility of requester increases as the augment of workers while the utility of workers decreases. It can be seen that the utility of requesters in non-SN is better than that in TMC-SN, but the utility of workers in non-SN is worse.    This demonstrates that the concern in Team Cohesion is profitable for workers but disadvantageous for requesters. Figure 2(c) shows that the Social Welfare of TMC-SN and non-SN is fluctuant. However, Social Welfare in TMC-SN performs better than non-SN as a whole. The concern in Team Cohesion is serviceable in teams of Social Welfare.

Conclusion
In this paper, we discuss the complex task assignment in crowdsourcing where the workers are in a social network. The TMC-SN mechanism is designed to solve the challenges in this scenario. In order to find out the most appropriate team, TMC-SN measures Worker Fitness of the worker for the team from both Marginal Contribution and Team Cohesion. The payment rule follows Myerson theorem. The theoretical analysis has proved that TMC-SN achieves truthfulness, individual rationality, and budget balance. In performance evaluation, the truthfulness of TMC-SN is further verified. We also compare the performance between TMC-SN and non-SN. The evaluation results show that TMC-SN is advantageous in terms of Social Welfare and favorable for the workers.