Discounting
A payoff received later is worth less than the same payoff now, and how fast it shrinks decides how much the future weighs in today's choice.
Often misread asTreating the discount factor as a psychological fact about the player, so the argument turns into a debate about whether people really are that impatient.
How to see it
A pound next round is worth less than a pound now
A discount factor is the weight a player puts on next round's payoff relative to this round's. It can stand for impatience, or for the probability that the relationship carries on at all. Those two are mathematically interchangeable, which is why an uncertain horizon and an impatient player behave identically.
The checkIn most game-theoretic uses it is carrying the chance of another round, not a taste for jam today, and the threshold conditions should be read that way.
Try itSet a 0.9 chance of another round with no impatience whatsoever, then set certainty of another round with a weight of 0.9 on tomorrow. Write out the value of receiving 1 each round under each. The two numbers are the same.
Games that show it
Know these first
Leads on to
Easily confused with
Sources
- Samuelson, P. (1937). Review of Economic Studies 4(2), 155-161.
- Rubinstein, A. (1982). Econometrica 50(1), 97-109.