Coalition-based task assignment with priority-aware fairness in spatial crowdsourcing

Question

1. What are the key components of a spatial task in reward-based multiple task assignment?

2. What is the Reward Pricing Model (RPM) and how does it quantify the temporal constraints of tasks in a spatial crowdsourcing environment?

3. What is a minimal worker coalition?

4. How is the CTA problem NP-hard?

Accepted Answer

In reward-based multiple task assignment, a spatial task consists of several key components. These include location (s.l), publication time (s.p), expected completion time (s.e), and deadline (s.d). Additionally, each task is labeled with a required workload (s.wl) to complete the task. The workload is determined by the time taken to finish the task, denoted as WC(s). These components are crucial in assigning tasks to multiple workers and determining the rewards for each worker based on their performance and efficiency in completing the tasks within the given constraints.

Accepted Answer

The Reward Pricing Model (RPM) is an incentive mechanism used in spatial crowdsourcing to motivate workers to complete tasks on time. It takes into account the task's publication time, expected completion time, deadline, required workload, and maximum reward offered by the task requester. The RPM quantifies the temporal constraints of tasks by considering the completion time and real reward (actual payment for the task) when a task is completed by a worker coalition. The model uses a penalty rate to account for tasks that cannot be finished before their expected completion time but can be completed before their deadline. The RPM formula is expressed as R = WC(s) / (s.t e), where R represents the actual reward of task s when completed by workers in WC(s), and s.t e denotes the completion time of s given the worker coalition WC(s). The model ensures that if a task can be completed before its expected completion time, workers will obtain the maximum reward. However, if a task cannot be finished before its deadline, the reward may be reduced based on the penalty rate. The RPM helps in optimizing task completion time and reward distribution in a spatial crowdsourcing environment.

Accepted Answer

A minimal worker coalition (MWC) for task s is a subset of workers that cannot obtain a reward equal to RMWC(s). It is the smallest coalition that can achieve the maximum reward for a specific task. In the given example, {w1, w2, w5} is not a minimal worker coalition for task s1 because {w1, w2} can generate the same reward as {w1, w2, w5}. For task s4, {w6} is the minimal worker coalition as it can obtain the maximum reward without collaboration. Definition 6 (Spatial Task Assignment) explains the concept of spatial task assignment, which involves assigning tasks to minimal worker coalitions to maximize the total reward.

Accepted Answer

The CTA problem is NP-hard through a reduction from the 0-1 knapsack problem. Given a set C with n items, each item has a weight and value. The knapsack problem aims to maximize the value of selected items while not exceeding a maximum weight capacity. In the CTA problem instance, tasks are associated with publication times, expected completion times, deadlines, workloads, and maximum rewards. Workers can complete one workload each. By transforming the knapsack problem into a CTA problem instance, if we could solve the CTA problem efficiently, we could solve the knapsack problem efficiently, contradicting the fact that the knapsack problem is NP-hard. Therefore, the CTA problem is also NP-hard.

Accepted Answer

The concept of acceptance probability is introduced to find high-value task assignments. It considers the time utilization ratio of workers and the rate of return of tasks. By calculating the acceptance probability, we can determine the probability that a task assignment is accepted. This probability is based on the workers' workload, travel time, actual reward, and maximal reward. It helps in ensuring high time utilization ratio of workers and high rate of return of tasks, ultimately leading to efficient task assignments.

Accepted Answer

R MWC(s) represents the actual reward obtained by a worker coalition (MWC(s)) when performing task s. It is a crucial factor in determining the efficiency and effectiveness of task allocation. The reward value influences the decision-making process of assigning tasks to worker coalitions, as higher rewards are generally preferred. Additionally, R MWC(s) plays a role in optimizing resource allocation and maximizing overall productivity. By considering the reward values, researchers can analyze the impact of different task assignments on the performance of worker coalitions and identify strategies to enhance task completion and reward distribution.

Accepted Answer

The acceptance probability AP MWC(s) is influenced by the time utilization ratio of workers in M W C(s) and the rate of return of task s. A higher time utilization ratio and rate of return result in workers obtaining more rewards. Therefore, a higher acceptance probability indicates that workers in M W C(s) can obtain more rewards, making the task assignment (s, M W C(s)) more likely to be accepted. The acceptance probability ranges from 0 to 1, representing the likelihood of task acceptance based on these factors.

Accepted Answer

The equilibrium-based approach ensures stable coalitions by adopting a best-response method to reach a pure Nash equilibrium within a non-cooperative multi-player game. Workers aim to maximize their utility given the strategies of other workers, and the outcome depends on all workers' strategies. The approach models the problem as an exact potential game with at least one pure Nash equilibrium. The best-response algorithm updates workers' strategies sequentially and asynchronously based on their best-response utility functions, leading to a pure Nash equilibrium. In this state, workers voluntarily select assigned tasks, resulting in stable coalitions. However, the Nash equilibrium achieved may not be optimal, so a Simulated Annealing (SA) strategy is introduced to find a better equilibrium with higher total rewards. This ensures the stability and optimality of the formed worker coalitions.

Accepted Answer

In a strategic game, the utility function U i : ST - R represents the utility of player w i , which can be calculated as the total reward obtained by coalition MWC(s){w i }. The utility function is denoted as U i (st) R, where st is the joint strategy profile. The utility function is used to determine the best strategy for each player in the game. It takes into account the rewards obtained by different coalitions and the current task assigned to the player. The utility function helps players make decisions based on the potential outcomes and rewards of different strategies. It is an essential component in game theory and helps in finding Nash equilibriums in strategic games.

Accepted Answer

Yes, the CTA game is an Exact Potential Game (EPG). An EPG is defined as a strategic game with a function Ph mapping strategies to real numbers, ensuring that the expected utility of each player is maximized when they choose their best response. In the CTA game, the global potential function allows the incentives of all players to be mapped, leading to a pure Nash equilibrium. This means that for countable strategies, the best-response framework always converges to a pure Nash equilibrium. The existence of an exact potential function in the CTA game demonstrates its compliance with the definition of an EPG, making it a suitable candidate for further analysis and optimization in game theory research.

Accepted Answer

Yes, CTA is an exact potential game (EPG). To prove this, an exact potential function Ph(st) is defined, representing the total rewards for all tasks in S. This function depends on the strategy st i of each worker w i in coalition M W C(s). By satisfying Eq. 11, Ph(st) is an exact potential function, making the CTA game an exact potential game. Since EPGs have at least one pure Nash equilibrium, the CTA game also has pure Nash equilibriums. The joint strategy st * = (st * 1, ..., st * n) is reached, where each player's utility is maximized, resulting in a pure Nash equilibrium.

Accepted Answer

The best-response strategy for each worker w_i in Spatial Crowdsourcing (SC) is to find the best-response task that maximizes the reward increase within the coalition they are staying in. This is achieved by calculating the best-response task s* using Equation 13. The strategy involves selecting a task that provides the highest reward increase for the worker, considering the current strategies of other workers. If a worker's current strategy is doing nothing, they are assigned the best-response task s*. If a worker is already assigned a task w_i.st, the strategies of other workers in the coalition MWC(w_i.st) are updated based on their ability to complete the task together on time. This iterative process continues until a Nash equilibrium is reached, where no worker wants to change their strategy.

Accepted Answer

Simulated Annealing (SA) is a stochastic optimization procedure that takes random walks through the problem space at successively lower temperatures, looking for points with better results than the current local optimal point. In the context of task assignment, SA is employed to search for better approximations to the global optimal task assignment. The process involves updating each worker's strategy sequentially based on the given strategy set, with the goal of maximizing the utility function. SA is regarded as an efficient probabilistic scheme for solving discrete optimization problems, evolving a discrete-time inhomogenous Markov chain. The state x(k) represents the strategy combination of the workers at the kth iteration in Algorithm 2. Workers can change their current strategy at random, with an identical probability P st i, where st i is one of the other reachable tasks or null. The transition probability is computed using Eq. 15, which considers the utility of the current and update strategies, as well as the temperature at the kth iteration. As the temperature decreases, the strategy selection becomes more likely to choose a better strategy with higher utility. Although allowing task selection with a smaller utility may decrease the total utility, it has the potential to facilitate a better Nash equilibrium, which is validated by experiments in Sect. 6.

Accepted Answer

Yes, the best-response algorithm converges to a pure Nash equilibrium. The proof shows that the utilities of all workers are mapped onto a potential function, Ph. This mapping suggests that adjustments made by each worker to their strategy result in changes to both their utility and the potential function. In a potential game, workers update their strategies sequentially to maximize their utility using the best-response algorithm. This dynamic is equivalent to a local search on the potential function, leading to a local maximum, which corresponds to a Nash equilibrium. The study [25] has proven that in any finite potential games, the sequential updates with best-response dynamics always converge to a Nash equilibrium.

Accepted Answer

Simulated annealing optimizes the best-response algorithm by introducing randomness into the update process of workers' strategies. This randomness allows worker w i to change the current strategy on a random basis by using one of the other reachable tasks with probabilities. The process is 'heated' up before 'cooling' down, helping the potential function to avoid a local optimum and converge to a better Nash equilibrium. Liu et al. [21] demonstrate that the convergence of simulated annealing strategy can be guaranteed when the cooling schedule is set as Tem(k) = b log(k), where b >= D * is a positive constant. The convergence of the best-response algorithm with simulated annealing is slower than that of the best-response algorithm alone. In Sect. 6, experimental evidence is provided to support this statement and demonstrate that a pure Nash equilibrium can effectively be calculated.

Accepted Answer

Fairness is crucial in spatial crowdsourcing due to varying worker inputs, such as each worker's marginal contribution and online time. Unfair reward distribution can lead to demotivated workers, reduced working hours, or platform abandonment. To ensure fairness, the concept of marginal contribution-based value is introduced, and tasks are assigned using a priority-aware fairness metric that considers workers' online and travel time. This approach aims to distribute rewards equitably among coalition members, fostering trust and maintaining a motivated workforce on the SC platform.

Accepted Answer

Marginal Contribution-based Value is a measure of a worker's contribution to a coalition in a task assignment game. It is calculated as the weighted average of all marginal contributions of a worker to all possible worker sequences from the coalition. The formula for Marginal Contribution-based Value is EQUATION, where V(MWC(s), w i) represents the value of worker w i in worker coalition MWC(s). The marginal contribution d i (G) is defined in Eq. 17, where R G w i denotes the reward obtained by workers in G w i, and G denotes the worker sequence before worker w i joining G. The probability of each worker sequence occurring is equal to 1 |MWC(s)|!.

Accepted Answer

The marginal contribution-based value of worker w1 is calculated by summing the values of all possible combinations of w1 with other workers. From the given data, the marginal contribution-based value of w1 is 0.05. This value is obtained by adding the values of w1 in all possible combinations with w2, w4, and w2, w4, w1. The total reward obtained by the coalition {w1, w2, w4} is 2.77, and the rewards for w1, w2, and w4 are 0.05, 1.36, and 1.36, respectively.

Accepted Answer

Priority-aware fairness in SC considers the priority of workers based on their online time and contribution. It ensures that workers with different online times and contributions receive different rewards. The priority-aware utility (PAU) measures the priority-aware fairness, calculated using a scoring function and reward of workers in a coalition. The fairness function and priority value are used to determine a fair share among workers. This approach allows for flexible fairness by adjusting the greediness parameter, making it possible to tolerate differences in worker rewards. Overall, priority-aware fairness aims to achieve a more fair task assignment in SC.

Accepted Answer

To combine priority-aware fairness with total reward maximization, we improve greedy and equilibrium-based task assignment approaches. These approaches aim to maximize the total reward while considering priority-aware fairness as a constraint. By doing so, the assignment provides priority-aware fairness without sacrificing the total reward. This is achieved by adjusting the task assignment based on the priority of workers and the reward associated with each task. The goal is to ensure that workers with higher priority receive tasks that align with their capabilities and contribute to the overall reward, while also maintaining fairness among all workers. This approach allows for a more balanced and efficient task assignment process, benefiting both workers and the organization as a whole.

Accepted Answer

The priority-aware threshold, denoted as d g, is a user- or SC platform-specified value that ensures priority-aware fairness among workers. It is set to guarantee that a worker's priority-aware utility exceeds this threshold before joining a coalition. This threshold plays a crucial role in the priority-aware greedy approach, as it helps maintain a balance in task assignments and prevents any worker from being unfairly prioritized over others. By incorporating this threshold, the greedy approach becomes more equitable and ensures that workers are assigned tasks based on their priority-aware utility, ultimately improving the overall efficiency and effectiveness of the task assignment process.

Accepted Answer

The priority-aware equilibrium-based approach involves initializing the process with an available worker set and assigning workers randomly to tasks. The reachable task set is computed for each worker, and they update their strategies. Tasks are assigned based on best-response tasks or priority-aware utility. The priority-aware utility exceeding a threshold determines task assignment probability. This approach is formulated as an n-player strategic game, ensuring efficient task allocation in a priority-aware manner.

Accepted Answer

The online time of workers is generated uniformly from values in the range [-5, 0]. This ensures that workers are online before or at the current time. The uniform distribution allows for flexibility in the online time of workers, accommodating different scenarios and workloads. By setting the range from -5 to 0, the experiments can simulate various situations where workers may start their tasks at different times, reflecting real-world scenarios where workers may have different availability and response times. This range also helps in analyzing the impact of worker availability on the overall performance of the system. Overall, the uniform generation of online time in gMission allows for a comprehensive evaluation of the system's behavior under different conditions and contributes to the robustness of the experimental setup.

Accepted Answer

Coalition-based task assignment involves workers forming coalitions to perform tasks through collaboration. Establishing worker coalitions is crucial for enhancing combined capabilities and improving utility. Fairness and priority awareness are important factors in coalition-based task assignment. Basik et al. [9] proposed a fair task allocation solution focusing on distributive fairness, while Ye et al. [36] aimed to maximize minimum utility for all workers. Zhao et al. [39] proposed a preference-aware task assignment problem for on-demand taxi dispatching. Cheng et al. [2] designed a game-theoretic approach to cooperative task assignment, but their approach differs from ours in terms of objectives and problem setting. Our goal is to maximize overall rewards with priority-aware fairness as a constraint, considering workers' rewards to motivate them to perform tasks. We aim to achieve a better Nash equilibrium with higher total rewards through a combination of simulated annealing scheme and the best-response method.

Accepted Answer

Future research directions for CTA algorithms include parallelizing the solutions for data-intensive applications, improving the efficiency of equilibrium-based approaches through lazy updating of best responses, generating optimal task execution schedules for maximum rewards, and exploring more efficient means of calculating marginal contribution-based values. These directions aim to enhance the scalability, efficiency, and fairness of CTA algorithms in spatial crowdsourcing tasks.

Coalition-based task assignment with priority-aware fairness in spatial crowdsourcing

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Most frequently asked questions

1. What are the key components of a spatial task in reward-based multiple task assignment?

2. What is the Reward Pricing Model (RPM) and how does it quantify the temporal constraints of tasks in a spatial crowdsourcing environment?

3. What is a minimal worker coalition?

4. How is the CTA problem NP-hard?

5. What is the concept of acceptance probability?

6. What is the significance of R MWC(s) in task performance?

7. What factors influence the acceptance probability AP MWC(s)?

8. How does the equilibrium-based approach ensure stable coalitions?

9. What is the utility function in a strategic game?

10. Is the CTA game an Exact Potential Game (EPG)?

11. Is CTA an exact potential game?

12. What is the best-response strategy in Spatial Crowdsourcing?

13. How does Simulated Annealing (SA) optimize task assignment in discrete optimization problems?

14. Does the best-response algorithm converge to a pure Nash equilibrium?

15. How does simulated annealing optimize the best-response algorithm?

16. Why is fairness important in spatial crowdsourcing?

17. What is the concept of Marginal Contribution-based Value?

18. What is the marginal contribution-based value of worker w1?

19. What is priority-aware fairness in SC?

20. How to combine priority-aware fairness with total reward maximization?

21. What is the priority-aware threshold in the greedy approach?

22. What is the process of priority-aware equilibrium-based approach?

23. What is the range for online time generation in gMission?

24. What is coalition-based task assignment?

25. What are the future research directions for Coalition-based Task Assignment (CTA) algorithms?

Citations

Task Assignment with Efficient Federated Preference Learning in Spatial Crowdsourcing

Task Recommendation in Spatial Crowdsourcing: A Trade-Off Between Diversity and Coverage

Fair and Efficient Ridesharing: A Dynamic Programming-based Relocation Approach

Optimizing Crowdsourcing Task Assignment Policies Using Multi-Agent Reinforcement Learning in Stochastic Games

<scp>WSC</scp>: A Crowd‐Powered Framework for Mapping Decomposable Complex‐Task With Worker‐Set

References

Optimization by Simulated Annealing

Equilibrium points in n-person games

Game Theory : Analysis of Conflict

REGULAR ARTICLEPotential Games

Algorithmic Game Theory: Quantifying the Inefficiency of Equilibria

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