Revenge feels extremely sweet. Most of us know what this feeling feels like. So what is the reason why taking revenge gives us so much pleasure ?

PET Scans
In the experiments carried out, the blood flow in the brains of the subjects was measured using positron emission tomography (PET). Water showing a certain sign was injected into the veins of each subject participating in the study, and then the person's brain was imaged when the water was carried through the blood and reached the brain. An increase in cerebral blood flow in a particular brain area means more brain activity and more oxygen consumption in that area. In the experiment, the brain activities of male subjects who participated in a game based on money exchange were scanned. According to the game rule; if a player made an individualistic choice based on self-interest rather than the common good, the other player would have the right to punish that person. The vast majority of players were seen choosing to impose a penalty even if it cost them some of their own money. Such punishment was found to cause activation of the caudate nucleus in the dorsal striatum, a region of the brain responsible for pleasure or gratification.
During the experiments, brain scans also revealed a correlation between a person's brain activity and how much they choose to punish based on their own detriment. It was observed that individuals with stronger activation were willing to inflict more harm to punish others. The diversity in the dorsal striatum region of the brain also causes diversity in behavior. Subjects with a lower activation in the dorsal striatum were less punishing.
Emotional Balance
Altruistic punishment seems irrational in terms of self-interest. But the study does explain this irrational behavior by showing that punishing the altruist may be a passion that sows the seeds of revenge, rather than a "meal best served cold." Activation in the dorsal striatum is a reflection of the pleasure expected as a result of punishing those who break social rules. So as activation increases, people become more willing to punish. In addition, a second region of the brain, the prefrontal cortex, is activated when it comes to evaluating pleasure from punishment versus the cost of punishment. That is, the heavier the price of punishment, the lower the severity of the punishment.
It seems that when we suffer harm from a person or group, the feeling of revenge causes an expectation in the reward centers of our brain, and when punishment occurs, it activates the pleasure and satisfaction regions of our brain.