the king and i-robot

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Rendezvous Problem

The rendezvous dilemma is related to the prisoner's dilemma and can be formulated in this way:

Two young people have a date in a park they have never been to before. Arriving separately in the park, they are both surprised to discover that it is a huge area and consequently they cannot find one another. In this situation each person has to choose between waiting in a fixed place in the hope that the other will find them, or else starting to look for the other in the hope that they have chosen to wait somewhere.

If they both choose to wait, of course, they will never meet. If they both choose to walk there are chances that they meet and chances that they do not. If one chooses to wait and the other chooses to walk, then there is a theoretical certainty that they will meet eventually; in practice, though, they would need an infinite amount of time for it to be guaranteed. The question posed, then, is: what strategies should they choose to maximize their probability of meeting?

Examples of this class of problems are known as rendezvous problems.

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