In this letter, a multi-user cooperative computing framework is applied to enable mobile users to utilize available computing resources from other neighboring users via direct communication links. An incentive scheme based on Bertrand game is proposed for the user to determine who and how to cooperate. We model the resource demand users as buyers who aim to use minimal payments to maximize energy savings, whereas resource supply users as sellers who aim to earn payments for their computing resource provision. A Bertrand game against buyer's market is formulated. When the users have complete information of their opponents, the Nash equilibrium (NE) of the game is obtained in closed form, while in the case of incomplete information, a distributed iterative algorithm is proposed to find the NE. The simulation results verify the effectiveness of the proposed scheme.