Revenge is an example of the sunk costs fallacy. Forgiveness is a decision to move forward regardless of sunk costs.

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The Paradox of Revenge
Revenge originates from the primal need for self-defense. In today's world, it is often abused as a destructive and futile response to anger or humiliation. . . .
Most strategies for revenge fail because they attempt to change the past. Unfortunately once the damage is done and the injury, insult, humiliation, or other loss occurs, the clock cannot be turned back and the loss is permanent. In addition, the value of the loss to the offended is seen as much greater than any benefit gained by the offender. As a result the offense represents an unrecoverable loss to society as a whole. Successful strategies for revenge look far into the future and recognize that the cycle of vengeance and retaliation can only spiral toward tragedy and are best stopped before they are started..
Revenge is a doomed attempt to eliminate shame and increase stature by asserting dominance. It fails because asserting dominance does not increase stature, instead it usually increases violence. Also, remorse cannot be coerced, it has to be discovered.
Evidence indicates that forgiveness increases self-esteem and decreases anxiety.
Sunk Costs
Economics and business decision-making recognize sunk costs as the costs that have already been incurred and which can never be recovered to any significant degree. Economic theory proposes that a rational actor does not let sunk costs influence a decision because past costs cannot be recovered in any case. This is also called the bygones principle; let bygones be bygones. This recognizes that you cannot change the past. The fallacy of sunk costs is to consider sunk costs when making a decision. Sound business decisions are based on a forward-looking view, ignoring sunk costs.
Revenge is an attempt to recover sunk costs; it is an example of the sunk costs fallacy. Forgiveness is a decision to move forward regardless of sunk costs. Sound emotional decisions, like sound business decisions, are based on a forward-looking view.

http://www.emotionalcompetency.com/revenge.htm