The only information each person has it their own coin, so their strategy is a pair of functions (f,g) from bits to bits, where either fx=y or gy=x (or both) fo

The only information each person has it their own coin, so their strategy is a pair of functions (f,g) from bits to bits, where either fx=y or gy=x (or both) for any bits x and y. There are only four possibilities for f, so picking, at random, f=id, gives g immediately.