Optimal resource allocation among areas of equal value

This paper considers a two sided resource allocation game in which both players have a fixed number of indivisible units which must be distributed over areas of equal value. A restriction for both sides is that there is only a limited number of choices for the number of units which may be assigned to any given target. A method of solution is presented for the case in which both sides have up to three such choices, and an example is provided to illustrate the theory.