why in the interest rate important in the discount rate

Question

i am currently studying the grim-trigger strategy and noticed that to discount the present values of payoffs, you need to discount them by the interest rate.

why in the interest rate used in such cases to discount?

also, would a low interest rate lead to collusion or deviation?

thanks!!

Answer 1

A dollar today is worth more than a dollar a year later, i.e., $1+r$, due to interest rate $r$.

Conversely, a dollar payoff in a year is worth less than a dollar today, i.e., $\frac {1}{1+r}$. The interest rate becomes the discount rate in this reverse measurement.