"The Talk" part 1

Birds do it, Bees do it, Humans do it.

Being the social animals that we are, sex is a normal part of everyday human existance. But why is "the Talk" stereotyped to the point where parents are unwilling to say a thing? The extent of a talk I got was, almost verbatim: "Don't be stupid. Use a condom."

There must be some sort of game going on here.

PLAYERS: Parents we will refer to as one player, for simplicity's sake. Child will be another player. We will assume that the child is around 11 years old because most schools start their sex-ed courses then. Peers will be another player, because as the stereotype goes, kids learn more from their friends about sex than their parents.

ACTIONS: Parents have a continuum of actions, reprsenting the amount of information to provide. This info will be represented with the letter i, and will belong to the closed interval [0,1], i=0 means the parents tell nothing, i=1 means they tell everything(anyone have a doctor as a mother/father?).
Peers will likewise have a continuum of actions, but kids can be a font of very unreliable info. Their info will be represented by the letter p, and will belong to the closed interval [-1/2, 1/2]. p=0 again represents no info. p=-1/2 means REALLY bad info, p=1/2 means decent info.
Now for the Child. They will have an choice of being sexually active or not, with the outcome/utility of that being a random number dependent on the info available, and their choice dependent on the info they have. Due to sex-ed, we will assume that the Child has an initial info of 1/4.

GAME: There is a cost for the Parents associated with giving the talk, possibly representing embarrassment or awkwardness. We will say that the cost is equal to the info given. Parents will also have a cost if the Child becomes sexually active and becomes pregnant(or gets someone pregnant) or gets an STI, which we will say is -10. Parents will have a benefit associated with their child becoming sexually active and having a healthy relationship(though this may be unrealistic, it helps ensure that the parents can have positive utility), which we will say is 2.
The Peers get a benefit for any p=/=0(bragging) that is equal to |p|(It doesn't matter how good the info is, but how much you have). They likewise, however, get a cost associated with their friend getting pregnant/STI that we will say is -5(not as bad as parents, but still sucks).

Now for the interesting part, the Child. We will assume that, like many kids, that they don't listen much to what their parents say, so i is only worth 1/2 of its value. We will also assume that, like many kids, they trust their friends. Hence, p is worth its absolute value. Total info, T, is therefore equal to 1/4 + |p| + (1/2)i. We are, unfortunately, assuming that all of this info is independent, which is not terribly accurate, but it makes the math much easier.

So, the Child will always become active if T > 1. They have lots of info and are just waiting to try it out.
The Child for sure will not become active if T < 3/4. They just aren't sure and need more info.
If T is in [3/4, 1], then they will pecome active with probability T.

The outcome for the Child of all this is
Not Active: 0. No change.
Active, but problems arise(pregnancies/STIs/whatever): -5
Active, but no problems arise: 2. Sex is fun, I ain't gonna lie.
Active, no problems, healthy relationship: 5. Sex is even better with love.(oh man, do I sound sappy)

Now, for some PROBABILITIES.
Problems: 1/4 + p + i. If you're well informed, problems are unlikely. If this total is <0, then treat it as 0, can never be more than .99 as there is always the possibility for a problem. "Failing" this probability roll means a problem arose.
Healthy relationship: 1/4 + i. As much as kids may not realise it, the parents probably know a fair bit about relationships. This total is never treated as greater than .95 because, again, some people are just unlucky.

This is a pretty big pill to swallow, but is a decent starting point. In the next part, I'll talk strategies.