 Most contemporary investigations the IPD take it to be neither infinite nor of fixed finite length but rather of indeterminate length. This is accomplished by including in the game specification a probability \(p\) (the “shadow of the future”) such that at each round the game will continue with probability \(p\). Alternatively, a “discount factor” \(p\) is applied to the payoffs after each round so that nearby payoffs are valued more highly than distant ones. Mathematically, it makes little difference whether \(p\) is regarded as a probability of continuation or a discount on payoffs. The value of cooperation at a given stage in an IPD clearly depends on the odds of meeting one's opponent in later rounds. (This has been said to explain why the level of courtesy is higher in a village than a metropolis and why customers tend leave better tips in local restaurants than distant ones.) As \(p\) approaches zero, the IPD becomes a one-shot PD, and the value of defection increases. As \(p\) approaches one the IPD becomes an infinite IPD, and the value of defection decreases. It is also customary to insist that the game has the property labeled RCA above, so that (in the symmetric game) players do better by cooperating on every round than they would do by “taking turns” — you cooperate while I defect and then I cooperate while you defect.