A sociopath is an individual that lacks the ability to feel empathy toward others. They do not have the capacity to feel remorse for wrongs they commit and are apt to engage in activities that are illegal. However, certain so-called "high-functioning" sociopaths may be able to mask these behaviors by pretending to be normal and falsely claim to feel empathy for others.
Shin Megami Tensei: Persona 4
The Persona 4 police detective Tohru Adachi is a textbook example of sociopathic behavior. Though he puts on an act as a bumbling, inexperienced detective that commonly runs his mouth, spilling pertinent investigation details that should remain secret, he is in fact the serial killer that the investigation team has been hunt for all along. He abuses his position on the police force to get close to both Mayumi Yamano and Saki Konishi, only to become enraged when they reject him and kills them both by sending them to the TV World. Entirely self-centered and misogynistic, his goofball poker face hides his frustration at being stuck in Inaba as punishment for a previous, undisclosed incident.
The Origami Killer of Heavy Rain lost his brother in a tragic accident when they were boys, largely because their abusive, uncaring father refused to help. The incident left him psychologically scarred, and as an adult, he enacts a scheme to test the devotion of fathers of similarly-aged boys. With no empathy for the children he kidnaps, his focus is entirely on seeing that his chosen fathers put themselves through immense suffering in order to rescue their sons. But even when Ethan Mars manages to pass the killer's trials and rescues his son Shaun, the killer attempts to do away with Ethan anyway.