jmc

We can calculate the total number of wins ($1$'s) by seeing how many matches were players, which is $12$ matches played. Then, we can calculate the # of wins already on the table, which is $5+3+2=10$, so there are $12-10=2$ wins left in the mystery player. Now, we will make the key observation that there is only $2$ wins ($1$'s) per column as there are $2$ winners and $2$ losers in each round. Strategically looking through the columns counting the $1$'s and putting our own $2$ $1$'s when the column isn't already full yields $\boxed{\text{000101}}$.