Normally, each female has only one mate per season, so everyone knows who the father of each child is. This simplifies play, but does not reflect the real world.
All kinds of allowances can be made for polyandry, clandestine sex, and so on. The female always has the option to remain monogomous - in which case she knows who the father of her child is. However, the father can never be sure.
In cases where the female has had more than one partner, the referee makes a random determination about who the father is, possibly weighted in favor of "legitimate" partners who have more opportunity to pass on their genes. Only at the end of the game, if then, are parentages revealed. Perhaps all the males learn is how many children they had . . .
Some sociobiologists speculate that this potential for uncertainty is no accident. A child may have a better chance of surviving if more than one males think they may be its father!