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I'm interested to know economic justifications of forgetting in various fields.

On example is Green and Porter(1984). To sustain a Cartel, Cartel members have incentive to forget deviations in a sufficiently distant past.

Another is Ekmekciy(2011) which shows that a rating system works better if it stops publicize misconducts, once they're old enough.

Literature on a more abstract level is also welcomed, e.g. results like it's more socially desirable in a dynamic games, some agents are restricted to stationary strategies.

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Maybe not what you are looking for, but a related concept is regret. Orphanides and Zervos (1995) is a classic paper on rational regret in a health economics concept http://www.jstor.org/discover/10.2307/2138580?uid=3739840&uid=2&uid=4&uid=3739256&sid=21106216442271

There's also plenty of irrational regret papers, mostly just boiling down to hyperbolic discounting models.

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  • $\begingroup$ Regret aversion seems somewhat orthogonal to agents which "forget". Forgetfulness seems to be much better modeled by imperfect recall in games. $\endgroup$
    – HRSE
    Sep 25 '15 at 2:56
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This topic has been studied widely in the theory of repeated games. See for example:

Robert J. Aumann, Sylvain Sorin: Cooperation and bounded recall, Games and Economic Behavior, Vol. 1, No. 1. (March 1989)

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