# Games With Finite Resources

### Thomas S. Ferguson and Costis Melolidakis

#### Abstract:

Games with Finite Resources as defined by Gale (1957) are two-person zero-sum
N-stage games in which each player has N resources and may use each resource once
and only once in the N stages. Gale's theorem on these games is generalized in several
directions. First the payoff is allowed to be any symmetric function of the stage
payoffs. Second, the players are allowed some latitude in choosing which game is
being played. Applications are given to some open questions in the area of Inspection
Games. Finally the payoff is allowed to be random, thus incorporating a result of Ross (1972) on Goofspiel. Application is made to a game-theoretic version of the
Generalized House Selling Problem.