This paper considers the setting where a cloud server services a static set or a dynamic sequence of tasks submitted by multiple clients. Every client wishes to assure honest execution of tasks by additionally employing a trusted third party (TTP) to re-compute the tasks with a certain probability. The cloud server makes a deposit for each task it takes, each client allocates a budget (including the wage for the server and the cost for possibly hiring TTP) for each task submitted, and every party has its limited fund for either deposits or task budgets. We study how to allocate the funds optimally to achieve the three-fold goals: a rational cloud server honestly computes each task; the servers wage is maximized; the overall delay for task verification is minimized. We apply game theory to formulate the optimization problems, and develop the optimal or heuristic solutions for three application scenarios. For each of the solutions, we analyze it through either rigorous proofs or extensive simulations. To the best of our knowledge, this is the first work on optimizing fund allocation for verifiable outsourcing of computation in the setting of one server and multiple clients, based on game theory.
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