How do I find my wife in a supermarket?

Question

If two people are lost in a maze, is there an algorithm that they can both use to find each other without having previously agreed what algorithm they will be using?

I think there are some characteristics that this algorithm will have:

• Each person must be able to derive it using logic that makes no assumptions about what the other person is deciding, but as each person knows the other is in the same position they may make deductions about what the other must be deciding.
• An identical algorithm must be derived by both people as there is total symmetry in their situations (neither has any knowledge about the starting position of the other, and the maze is a fixed size, and fully mapped by both). Note that the algorithm is not required to be deterministic: it is allowed to be randomized.