Interesting HI/LO game dilemma (not poker)

So, the local radio station has a game called HI LOW. Basically, they pick a random (or is it really random?) number between 100 and 1000, then 15 callers get to call in. Each one guesses the number, and if they get it right, they win that ammount in dollars. If they get it wrong (as is likely the case), they are told that the true number is either HIGHER or LOWER than the guess.

This problem occurred to me when I heard the first caller guess 550. At first, this seems like a reasonable guess --but only if this caller were allowed to make all 15 guesses himself. Knowing that each caller only gets one guess, then mathematically it would be correct for the first person to guess 1000, the 2nd person to guess 999, etc. However, although this is the optimal strategy for each individual caller, it means that as a whole the callers will only win money 15/900 of the time. If they used correct strategy as a whole, they could beat the system and win money every time (by guessing the middle of the two known numbers that it is below and higher than). So, either the first caller is an altruist or doesn't understand game theory. Or perhaps I'm missing something. Either way, I thought it was interesting to see that the optimal strategy for each individual caller ended up being the worst strategy cumulatively (or exactly what the radio station would want you to do).

Discuss

-Grant