As the amount of data collected for crowdsensing applications increases rapidly due to improved sensing capabilities and the increasing number of Internet of Things (IoT) devices, the cloud server is no longer able to handle the large-scale datasets individually. Given the improved computational capabilities of the edge devices, coded distributed computing has become a promising approach given that it allows computation tasks to be carried out in a distributed manner while mitigating straggler effects, which often account for the long overall completion times. Specifically, by using polynomial codes, computed results from only a subset of devices are needed to reconstruct the final result. However, there is no incentive for the edge devices to complete the computation tasks. In this paper, we present an all-pay auction to incentivize the edge devices to participate in the coded computation tasks. In this auction, the bids of the edge devices are represented by the allocation of their Central Processing Unit (CPU) power to the computation tasks. All edge devices submit their bids regardless of whether they win or lose in the auction. The all-pay auction is designed to maximize the utility of the cloud server by determining the reward allocation to the winners. Simulation results show that the edge devices are incentivized to allocate more CPU power when multiple rewards are offered instead of a single reward.