This was done on a much larger scale (without primes) as a lottery game in Sweden called "Limbo" or "LUPI" (lowest unique positive integer). Several game theorists have analyzed the data with some interesting results:
Calculating the equillibrium strategy for rational actors is difficult because each player doesn't know how many other players there are. In the paper above, game theorists calculate it and show that the distributions seen in the lottery match up fairly well to a rational strategy.
http://swopec.hhs.se/hastef/abs/hastef0671.htm
Calculating the equillibrium strategy for rational actors is difficult because each player doesn't know how many other players there are. In the paper above, game theorists calculate it and show that the distributions seen in the lottery match up fairly well to a rational strategy.