Discount Factor

In game theory and economics, the discount factor (typically denoted δ) is a number between zero and one that measures how much a player values a payoff received in the future relative to the same payoff received today. A discount factor of δ = 0.9 means that a payoff of 1 tomorrow is worth 0.9 today; a discount factor of δ = 0 means the player cares only about the present.

The discount factor is the hidden variable that determines whether cooperation is possible in repeated games. The Folk Theorem requires that the discount factor be high enough that the long-term benefits of cooperation outweigh the short-term temptation to defect. When δ is low — when players are impatient, when interaction is uncertain, or when the time between rounds is long — cooperation collapses because the shadow of the future is too short to sustain trust.

The concept extends beyond formal game theory. In ecology, the discount factor captures how much an organism values future reproduction relative to present survival. In behavioral economics, it explains why humans systematically undervalue future rewards, a phenomenon known as hyperbolic discounting. In climate policy, the discount factor is the parameter that determines whether present generations are willing to pay for benefits that will accrue centuries hence. The discount factor is not a technical detail. It is the mathematical expression of how much the future matters.