  Direct reciprocity is a mechanism for the evolution of cooperation in
repeated social interactions. According to this literature, individuals
naturally learn to adopt conditionally cooperative strategies if they have
multiple encounters with their partner. Corresponding models have greatly
facilitated our understanding of cooperation, yet they often make strong
assumptions on how individuals remember and process payoff information. For
example, when strategies are updated through social learning, it is commonly
assumed that individuals compare their average payoffs. This would require them
to compute (or remember) their payoffs against everyone else in the population.
To understand how more realistic constraints influence direct reciprocity, we
consider the evolution of conditional behaviors when individuals learn based on
more recent experiences. Even in the most extreme case that they only take into
account their very last interaction, we find that cooperation can still evolve.
However, such individuals adopt less generous strategies, and they tend to
cooperate less often than in the classical setup with average payoffs.
Interestingly, once individuals remember the payoffs of two or three recent
interactions, cooperation rates quickly approach the classical limit. These
findings contribute to a literature that explores which kind of cognitive
capabilities are required for reciprocal cooperation. While our results suggest
that some rudimentary form of payoff memory is necessary, it already suffices
to remember a few interactions.
