Nash Equilibrium in Macro-Task Crowdsourcing Systems With Collective-Effort-Dependent Rewarding

Macro-task crowdsourcing systems are often used successfully to collaboratively accomplish complicated tasks by employing a large number of workers. However, recent observations suggest that workers' free riding can seriously hinder the success of macro-task crowdsourcing. Thus far, most of previous works study this problem by considering that involved workers can always obtain the total reward provided by the requester, which collides with many realistic situations. Here we consider an S-shaped reward function to faithfully depict the dependence of obtaining the reward from the requester on the collective efforts of workers. Furthermore, to properly model the interaction between the requester and workers, we apply the Stackelberg game description, where the former is the leader while the latter group are the followers. By using backward induction, we show that there is a unique Nash equilibrium in the classical game framework. In the scenario of evolutionary games, by considering dynamical interactions, we also identify a unique Nash equilibrium. Our analytical predictions are confirmed by numerical calculations, which underline that workers' efforts can be increased by increasing the steepness parameter of the reward function. Hence, such collective-effort-dependent rewarding can effectively motivate workers to avoid a free-rider choice.