Note: If you understand up to Stage 1 of this post, you now understand how allele frequencies are determined in a population that has random mating and a few other biology related assumptions. The invisible "Players" choose which allele it is better to be, and they will settle onto an equilibrium as Manfred describes.
The above post contains everything you need to do some intro-level population genetics problems. If you learned something from the above most and would now like to test your shiny new genetics skills, here's a problem set:
Suppose A and B are the only two alleles in a diploid genome, and AA has fitness 2, BB has fitness 1, and AB has fitness 3
Problem: What proportion of alleles are A? What proportion of alleles are B?
Bonus question: What will the final distribution of AA, AB, and BB prototypes look like?
In practice for biologists, you'd be doing this problem backwards - looking at the percent of the population that expresses each phenotype, and using that to infer allele frequencies and relative fitness. If I tell you that 25% of a population has sickle cell, if you know that sickle cell disease comes from a homozygous recessive allele, and if you are willing to assume various things, that's all you need to work backwards all the way to the payoff matrix.
In practice, of course, mating isn't random. If AB is inferior to both AA and BB, then there is an incentive for A carriers to avoid B carriers and it is a trend towards speciation. If AB is superior to both AA and BB, there is an incentive for heterozygosity.) Also in practice, the allele frequencies are constantly shifting so you are following a moving target, and sometimes sampling is biased (for example, carriers of low fitness alleles die before you can measure them) etc.
Suppose that Red got to move first. There are some games where moving first is terrible - take Rock Paper Scissors for example. But in this game, moving first is great, because you get to narrow down your opponent's options! If Red goes first, Red picks 'A', and then Blue has to pick 'B' to get a cookie.
This is basically kidnapping. Red has taken all three cookies hostage, and nobody gets any cookies unless Blue agrees to Red's demands for two cookies. Whoever gets to move first plays the kidnapper, and the other player has to decide whether to accede to their ransom demand in exchange for a cookie.
What if neither player gets to move before the other, but instead they have their moves revealed at the same time?
Pre-Move Chat:
Red: "I'm going to pick A, you'd better pick B."
Blue: "I don't care what you pick, I'm picking A. You can pick A too if you really want to get 0 cookies."
Red: "Okay I'm really seriously going to pick A. Please pick B."
Blue: "Nah, don't think so. I'll just pick A. You should just pick B."
And so on. They are now playing a game of Chicken. Whoever swerves first is worse off, but if neither of them give in, they crash into each other and die and get no cookies.
So, The Question: is it better to play A, or to play B?