Frequency based discounting of values Let's say there are two products A and B both of which have some value.
Consider a population of 10.000 people choosing between these two products. 
I would like to come up with a function that adjusts the price of A and B based on the frequency of people choosing the products.
The function should satisfy the following criteria:
1. The value of A and B should always sum to 1 and be in the range between 0 and 1.
2. The more people are choosing a product the lower should its value be and similarly the fewer people are choosing a product the higher should its value be.
To illustrate let's say that 
on day 1: 6000 people are choosing product A and 4000 are choosing product B 
and their value is 0.6 and 0.4
respectively.
on day 2: 7000 people are choosing product A and 3000 are choosing product B the value of A should decrease and the value of B should increase.
3. The adjustment of the value should not be linearly increasing or decreasing based on the frequency of people using the product but the increase or decrease should be steeper when the proportion of people using the products is close to 50% but should increase or decrease slower when the people choosing the products is skewed (e.g. 90 vs. 10%).
 A: Well I based my function on the logistic curve.
I used $A = \frac{1}{1+e^{(N_a-5000)/1000}}$ where $N_a$ is the number of people choosing product A. And B would simply be, $B=1-A$
The 1000 in the denominator of the exponent can be changed to say 10000 or 5000, but the larger this number is, the slower the change will be.
Here are some example values using 1000 in the denominator, 
$N_a=5000 \rightarrow A=0.5, B=0.5$ 
$N_a=6000 \rightarrow A=0.27, B=0.73$ 
$N_a=7000 \rightarrow A=0.12, B=0.88$
$N_a=8000 \rightarrow A=0.05, B=0.95$
$N_a=9000 \rightarrow A=0.02, B=0.98$ 
And this function is symmetric around 5000 so,
$N_a=5000 \rightarrow B=0.5, A=0.5$ 
$N_a=4000 \rightarrow B=0.27, A=0.73$ 
$N_a=3000 \rightarrow B=0.12, A=0.88$
$N_a=2000 \rightarrow B=0.05, A=0.95$ 
$N_a=1000 \rightarrow B=0.02, A=0.98$ 
Also, note the change is less steep near the edges as you requested (going from 2000 to 1000 results in less response change than when you go from 5000 to 4000).  The equation I used could be used for prices that quickly respond to market forces. Changing the 1000 in the equation to say, 10000 will make the prices of A and B much closer together, and would make the prices less responsive.  
