$A,B,C$ are playing a dice game. $A$ chooses a number from 1 to 30 first, then $B$ chooses another number from 1 to 30, finally $C$ chooses another number from 1 to 30. Therefore, the 3 numbers chosen are different. Then throw a 30 sided dice numbered from 1 to 30 with equal probability. The winner of the game is the one having the chosen number closest to the dice outcome. The winner will gain the number of dollars same as the dice outcome.
What is the optimal strategy for $A,B,C$ respectively? We assume that they all want to maximize their own expected payoff. I know the solution when we only have 2 people in the game. What about three people? Which player is in the most advantageous position?
How can we approach this problem?