  Coded distributed computing (CDC) has emerged as a promising approach because
it enables 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 edge servers can be used to reconstruct the final result.
However, incentive issues have not been studied systematically for the edge
servers to complete the CDC tasks. In this paper, we propose a tractable
two-level game-theoretic approach to incentivize the edge servers to complete
the CDC tasks. Specifically, in the lower level, a hedonic coalition formation
game is formulated where the edge servers share their resources within their
coalitions. By forming coalitions, the edge servers have more Central
Processing Unit (CPU) power to complete the computation tasks. In the upper
level, given the CPU power of the coalitions of edge servers, an all-pay
auction is designed to incentivize the edge servers to participate in the CDC
tasks. In the all-pay auction, the bids of the edge servers are represented by
the allocation of their CPU power to the CDC tasks. The all-pay auction is
designed to maximize the utility of the cloud server by determining the
allocation of rewards to the winners. Simulation results show that the edge
servers are incentivized to allocate more CPU power when multiple rewards are
offered, i.e., there are multiple winners, instead of rewarding only the edge
server with the largest CPU power allocation. Besides, the utility of the cloud
server is maximized when it offers multiple homogeneous rewards, instead of
heterogeneous rewards.

Computer Science and Game Theory;Distributed, Parallel, and Cluster Computing