A group of 7 players play the following game. Each writes down a positive integer that is less than 1000.

A group of 7 players play the following game. Each writes down a positive integer that is less than 1000. The player who writes down the smallest number is awarded a prize equal to the number of dollars equal to the number that she wrote down. If there is a tie for smallest number, the prize is divided equally among those who wrote the smallest number. Find the strategy or strategies that survive iterated deletion of strictly dominated strategies. Explain your answer.