In this paper, 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 textit{who} and textit{how} to cooperate. We model the resource demand users as textit{buyers} who aim to use minimal payments to maximize energy savings, whereas resource supply users as textit{sellers} who aim to earn payments for their computing resource provision. A Bertrand game against textit{buyers market} is formulated. When the users have textit{complete information} of their opponents, the Nash equilibrium (NE) of the game is obtained in closed form, while in the case of textit{incomplete information}, a distributed iterative algorithm is proposed to find the NE. The simulation results verify the effectiveness of the proposed scheme.
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