Acceptance rate is the probability the user perform the assigned task.
Some thoughts:
Option 1:
Intuitively, higher price means higher f. So f should monotonicity increase with higher price. Function like f = 1-1/(price+1) that asymptotically approaches 1.
Option 2:
We can use normal distribution, and that is called Cumulative Gaussian (Normal) Distribution.
http://stats.stackexchange.com/questions/158556/probability-of-agreeing-to-do-some-work-depending-on-the-payment,
Basically, we can chose sigma =(p2-p1)/2 or (p2-p1)/4, or 6, etc... It is more common to use normal distribution when we talk about stimulation.
Here is the cumulative distribution function (CDF) of a Gaussian with mean μ=(p1+p2)/2 and variance σ=(p2−p1)/6, which is of course monotonic in price (as all CDFs must be):
Acceptance rate is the probability the user perform the assigned task. Some thoughts:
Option 1: Intuitively, higher price means higher f. So f should monotonicity increase with higher price. Function like f = 1-1/(price+1) that asymptotically approaches 1.
Option 2: We can use normal distribution, and that is called Cumulative Gaussian (Normal) Distribution. http://stats.stackexchange.com/questions/158556/probability-of-agreeing-to-do-some-work-depending-on-the-payment, Basically, we can chose sigma =(p2-p1)/2 or (p2-p1)/4, or 6, etc... It is more common to use normal distribution when we talk about stimulation. Here is the cumulative distribution function (CDF) of a Gaussian with mean μ=(p1+p2)/2 and variance σ=(p2−p1)/6, which is of course monotonic in price (as all CDFs must be):