I love the premise of the Waag society’s new mobile learning game "Frequency 1550":
"The Amsterdam UMTS-network is interfering with a different time period:
the Middle Age. The city’s bailiff gets in contact with the 21st
century Amsterdam. He thinks the players are pilgrims coming to 1550
Amsterdam to visit a relic: the Holy Host associated with The Miracle
of Amsterdam. He promises an easy access to citizenship if players can
help him retrieve the holy relic which recently got lost."
Although, surely if people from the future are communicating with you through a crack in spacetime made by their futurephones, I’m not sure offering them freedom of the city would be your first thought.