Finite search games with multiple targets

We consider a class of zero-sum games played in a finite set of hiding places S. Player I (the Hider) hides some targets in a subset of S of size k, and Player II (the Searcher) searches the locations one-by-one until finding all the targets. The payoff of the game is given by some function f of the set of locations searched up until all the targets have been found. We give a sufficient condition on f for the game to have a simple closed form solution, and we give natural examples of games that satisfy this condition.

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