Crowdsourcing with Bounded Rationality: A Cognitive Hierarchy Perspective

Previous studies in crowdsourcing systems usually regard workers as fully rational players, who have infinite cognitive capabilities when reasoning about other players' decisions. However, recent psychological studies have revealed that humans are often bounded rational with cognitive reasoning limits. In this paper, we present a first study regarding the impact of such worker bounded rationality in a crowdsourcing system, and characterize how the result obtained from this more practical assumption deviates from the fully rational benchmark. Specifically, we consider a simple two-stage crowdsourcing model, where a requester first determines the rewards for workers completing the tasks, and then workers make their task choices accordingly. First, we show that such a model is non-trivial to analyze even in the fully rational case, due to the integer constraints on workers' choices. Nevertheless, we are able to characterize the closed-form solution of the optimal rewards and Nash equilibrium with full rationality by exploiting the special structure of the problem formulation. Next, we focus on the more practical bounded rational model, and apply the cognitive hierarchy theory from behavioral economics in the modeling of workers' decisions. Comparing with the fully rational benchmark, we show that in practice the requester can receive a higher profit when considering the workers' bounded rationality, especially when the number of workers is large or the workers' average cognitive level is low. When the workers' average cognitive level is high enough, however, the practical bounded rational model converges to the benchmark fully rational model.