# Contract-Based Incentive Mechanism for Mobile Crowdsourcing Networks
## 5 Numerical Results  
Numerical simulation results are presented to assess the proposed mechanism. Figure 3 demonstrates the MUs' optimal basic wage \(\alpha_{i}^{*}\), bonus coefficient \(\beta_{i}^{*}\) and crowdsourcing effort \(e_{i}^{*}\) with the same crowdsourcing cost \(c_{i}\). We notice that as \(\theta_{i}\) becomes large, the \(i\)th MU's profit per unit crowdsourcing effort increases; thus the optimal crowdsourcing effort \(e_{i}^{*}\) increases and the SP may allocate a greater bonus \(\beta_{i}^{*}\) to attract the MUs to offer enough crowdsourcing effort. Then, because \(\beta_{i}^{*}\) increases, the SP only needs to offer a lesser basic wage \(\alpha_{i}^{*}\) to the MUs for enough help. Figure 4 shows the performance of the crowdsourcing effort-incentive with three MUs. The simulation parameter setting is the same as for Figure 3. Each MU obtains its maximum utility by selecting the optimal crowdsourcing effort \(e_{i}^{*}\). Thus, in the proposed optimal contract, the SP can attract the MUs to take full responsibility for their crowdsourcing tasks. The proposed  
contract-based incentive mechanism breaks information asymmetry and attracts the MUs to make maximum crowdsourcing efforts. Figure 5 presents the MUs' optimal basic wage \(\alpha_{i}^{*}\), bonus coefficient \(\beta_{i}^{*}\) and crowdsourcing effort \(e_{i}^{*}\) with the same crowdsourcing profit \(\theta_{i}\). As shown in Figure 4, the MUs' optimal bonus coefficient \(\beta_{i}^{*}\) and the crowdsourcing effort \(e_{i}^{*}\) increase in the crowdsourcing cost coefficient \(c_{i}\). The MUs' optimal basic wage \(\alpha_{i}^{*}\) increases in the crowdsourcing cost coefficient \(c_{i}\). As \(c_{i}\) becomes large, the \(i^{th}\) MU's crowdsourcing cost increases; thus the SP may offer a greater basic wage \(\alpha_{i}^{*}\) to obtain enough crowdsourcing effort. Figure 6 shows the MUs' optimal bonus coefficient \(\beta_{i}^{*}\) with the various SP's risk-averse degree \(\eta_{S}\) and MUs' risk-averse degree \(\eta_{M}\); \(\theta_{i}\) is the same as that in Figure 3. We notice that the \(i\)th MU's optimal bonus coefficient \(\beta_{i}^{*}\) decreases in its absolute risk-averse coefficient \(\eta_{M}\) and increases in the SP's absolute risk-averse coefficient \(\eta_{S}\). Similar results can be obtained for cases of the MUs' optimal effort \(e_{i}^{*}\), which verifies Equations (24) and (26). Figure 7 illustrates the SP's optimal expected utility with the SP's variable risk-averse degree \(\eta_{S}\) and MUs' risk-averse degree \(\eta_{M}\). As the SP's variable risk averse degree \(\eta_{S}\) and the MUs' risk-averse degree \(\eta_{M}\) become large, the SP's optimal expected utility decreases. The greater the MUs' risk-averse degree \(\eta_{M}\), the lesser the SP's optimal expected utility. Thus, in order to obtain more utilities, the SP needs to choose MUs with a lesser risk-averse degree. Finally, by introducing another two mechanisms, we evaluate the proposed incentive mechanism. The first incentive mechanism is the contract-based mechanism in the presence of symmetric information (i.e., the SP obtains information about the MUs' crowdsourcing efforts). The second incentive mechanism is a _linear pricing_ scheme with \(\alpha_{i}=0\). In this linear pricing mechanism, the SP only specifies the performance-based bonus coefficient \(\beta_{i}\), without the basic wage. Figure 8 presents the SP's optimal expected utility with the different incentive mechanisms. In these three incentive mechanisms, the contract-based mechanism under the symmetric information scenario obtains the maximum expected utility of the SP, which is considered to be the upper bound on the SP's expected utility. Compared to the other two incentive mechanisms, the SP with the proposed  
Figure 4: Mobile users’ (MUs’) optimal utility with different types of effort-incentive design. contract scheme always achieves more utility than that with \(\alpha_{i}=0\).