The object of this study is to solve a resource sharing problem. One considers a surgery ward with a fixed number of beds. A team of surgeons is sharing this common scarce resource. Every working day a different surgeon has the possibility of admitting a number of elective patients, within the capacity of the ward, and operates on them. In the instance of an operation we assume that the surgeon payoff depends on the type of sickness to be cured. The problem is to find the admission policy that would prevail if the surgeons operate in a noncooperative manner and strive to maximize their long term expected discounted payoffs.

To solve this problem, we consider a class of discounted sequential games whose analysis if made with a contracting operator approach à la Denardo.

A successive approximation algorithm is used to prove the existence of and to compute a Nash eqyuilibrium defined in the class of pure strategies.