Editing Prisoner's dilemma (section)

=== General strategy ===
If the iterated prisoner's dilemma is played a finite number of times and both players know this, then the dominant strategy and Nash equilibrium is to defect in all rounds. The proof is [[Mathematical induction|inductive]]: one might as well defect on the last turn, since the opponent will not have a chance to later retaliate. Therefore, both will defect on the last turn. Thus, the player might as well defect on the second-to-last turn, since the opponent will defect on the last no matter what is done, and so on. The same applies if the game length is unknown but has a known upper limit.{{citation needed|date=May 2023}}

For [[cooperation]] to emerge between rational players, the number of rounds must be unknown or infinite. In that case, "always defect" may no longer be a dominant strategy. As shown by [[Robert Aumann]] in a 1959 paper,<ref>{{Citation |last=Aumann |first=Robert J. |title=Contributions to the Theory of Games (AM-40), Volume IV |chapter=16. Acceptable Points in General Cooperative n-Person Games |date=2016-03-02 |pages=287–324 |chapter-url=https://www.degruyter.com/document/doi/10.1515/9781400882168-018/html |access-date=2024-05-14 |publisher=Princeton University Press |language=en |doi=10.1515/9781400882168-018 |isbn=978-1-4008-8216-8}}</ref> rational players repeatedly interacting for indefinitely long games can sustain cooperation. Specifically, a player may be less willing to cooperate if their counterpart did not cooperate many times, which causes disappointment. Conversely, as time elapses, the likelihood of cooperation tends to rise, owing to the establishment of a "tacit agreement" among participating players. In experimental situations, cooperation can occur even when both participants know how many iterations will be played.<ref>{{cite journal |last1=Cooper |first1=Russell |last2=DeJong |first2=Douglas V. |last3=Forsythe |first3=Robert |last4=Ross |first4=Thomas W. |title=Cooperation without Reputation: Experimental Evidence from Prisoner's Dilemma Games |journal=Games and Economic Behavior |date=1996 |volume=12 |issue=2 |pages=187–218 |doi=10.1006/game.1996.0013}}</ref>

According to a 2019 experimental study in the ''American Economic Review'' that tested what strategies real-life subjects used in iterated prisoner's dilemma situations with perfect monitoring, the majority of chosen strategies were always to defect, [[Tit for tat|tit-for-tat]], and [[grim trigger]]. Which strategy the subjects chose depended on the parameters of the game.<ref>{{Cite journal|last1=Dal Bó|first1=Pedro|last2=Fréchette|first2=Guillaume R.|date=2019|title=Strategy Choice in the Infinitely Repeated Prisoner's Dilemma|journal=American Economic Review|language=en|volume=109|issue=11|pages=3929–3952|doi=10.1257/aer.20181480|s2cid=216726890|issn=0002-8282|url=https://www.aeaweb.org/articles?id=10.1257/aer.20181480}}</ref>