In a joint project, the project cost is allocated to the participants. How to allocate the cost has been discussed mainly in cooperative game theory assuming that the cost is certain. If the project cost is uncertain, each participant is exposed to the risk of allocated cost. Thus the risk should be allocated according to the risk acceptance level for each participant. For this risk allocation, a stochastic cooperative game is useful rather than a cooperative game based on the certainty of cost. We develop a contingent cost allocation scheme in which the risk is transferred mutually in order to attain efficient risk allocation by a stochastic cooperative game. As a result, the efficient risk allocation is derived so that all participants are better off than the allocation which does not transfer the risk mutually.