We propose a game theoretic framework for task allocation in mobile cloud computing that corresponds to offloading of compute tasks to a group of nearby mobile devices. Specifically, in our framework, a distributor node holds a multidimensional auction for allocating the tasks of a job among nearby mobile nodes based on their computational capabilities and also the cost of computation at these nodes, with the goal of reducing the overall job completion time. Our proposed auction also has the desired incentive compatibility property that ensures that mobile devices truthfully reveal their capabilities and costs and that those devices benefit from the task allocation. To deal with node mobility, we perform multiple auctions over adaptive time intervals. We develop a heuristic approach to dynamically find the best time intervals between auctions to minimize unnecessary auctions and the accompanying overheads. We evaluate our framework and methods using both real world and synthetic mobility traces. Our evaluation results show that our game theoretic framework improves the job completion time by a factor of 2-5 in comparison to the time taken for executing the job locally, while minimizing the number of auctions and the accompanying overheads. Our approach is also profitable for the nearby nodes that execute the distributor's tasks with these nodes receiving a compensation higher than their actual costs.