Trade of a problem-solving task

This paper focuses on a task allocation problem, particularly in cases where the task is to find a solution to a search problem or a constraint satisfaction problem. If the search problem is difficult to solve, a contractor may fail to find a solution. Here, the more computational resources, such as the CPU time, the contractor invests in solving the search problem, the more likely a solution will be found. This brings about a new problem in which a contractee has to find an appropriate quality level in task achievement as well as to efficiently allocate a task among contractors. For example, if the contractee asks the contractor to find a solution with certainty, the payment from the contractee to the contractor may exceed the contractee's benefit from obtaining a solution, which discourages the contractee from trading a task. However, it is difficult to solve this problem because the contractee cannot ascertain the contractor's problem-solving ability such as the amount of available resources and knowledge (e.g. algorithms, heuristics) nor monitor how many resources are actually invested in solving the allocated task. To solve this problem, we propose a task allocation mechanism that is able to choose an appropriate quality level in task achievement and prove that this mechanism guarantees that each contractor reveals its true information. Moreover, we show that our mechanism can increase the contractee's utility compared with a simple auction mechanism by using computer simulations.