## Game Theory 101 (#55): Discount Factors

gametheory101.com/courses/game-theory-101/

We need to explore infinite horizon games. However, if you add up an infinite string of a positive payoff, they all equal infinity regardless of the base value. Discount factors rescue us. Recognizing that consumption today is better than consumption tomorrow and the possibility that an interaction might not continue due to unforeseen circumstances, we use the discount factor to make tomorrow’s payoffs smaller than today’s.

Although we still end up with an infinite string of payoffs, they form something known as a geometric series. In the next lecture, we will see how geometric series have a clean closed-form solution that avoids the infinity problem.

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## 18 thoughts on “Game Theory 101 (#55): Discount Factors”

1. OrkTv says:

3:00 This is reminiscent of Pascal's wager. By the same reasoning, we can't be sure that we are visited by the mafia today and lose our money, in which case having the money tomorrow would be better. But I get the point that you're making. One question: how does the discount factor relate to the concept of positive affine transformations? A discount factor is very "numerical"; it doesn't seem in any way a product of our preference ordering.

2. Klaire Hoang says:

It's like every time a question pops up in my mind, you had already anticipated it and explained it so well in your video. I'm happier watching your video than some random Netflix show, wow the delicacy

3. Raikhan Amir says:

delta? are you kidding me? it is sigma. but thanks.. was helpful =)

4. N says:

You are amazing! Could not find any explanation of what a discount factor is in the German web… Thank you so much!

5. Huixtocihuatl says:

Can someone explain to me why he puts an exponent to delta? Don't you simply subtract delta from Delta when you switch period? Let's say Delta is 0,02, then 0,04 then 0,,06 because you add Delta from period to period. This is why I don't understand the exponent over the delta.

6. Huixtocihuatl says:

Came from Martin Skreli's video on finance lesson 2 https://www.youtube.com/watch?v=6rgGgCkEokU. When I saw that the discount rate was actually a limit to infinity I was so astonished! The day after, I found this video and it's amazing.

7. Posei77 says:

Thanks William Spaniel this has saved me

8. Darth Danksaber says:

You have a handsome voice & your oral chakra is creating healing orgone-ki in my biceps, thank you

9. Rafael Gonçalves says:

Just came from coursera. You made it way simpler to understand! Thanks 😀

10. Michael Esplin says:

Why not a limit of some average?

11. huynhtho dothi says:

very helpful, thanks a lot :')

12. Kirk Breiner says:

Wish my professor taught this well!!! Haha wait you are my professor!!

13. Hisham Ragheb says:

You explained the discount factor very rationally. Great work

14. Jose Lalo Guzman says:

bro you are such a crack. im from mexico and you are saving me during finals.

15. Luka Dacic says:

Thank you.

16. Gambiteer says:

17. markd315 says:

So the irony I've noticed with these games is that if Yahweh or some other god descended and announced the date of the end of the world, he would break so many Prisoner's dilemma and Stag hunt agreements, like peace treaties and free trade agreements that he may be creating it by doing so.

18. Sun God Moth says:

So basically in MathJax it's:
$sum_{i=0}^infty 3(delta^i)$
And in python:
k = 1
j = 1
delta = input('Enter a discount value.n')
while k == 1:
print 3*(delta**j)
j += 1