Jigsaw Killer

The Jigsaw Killer is a fictional character in the Saw film series. Jigsaw made his debut appearance as the primary antagonist in the first film of the series, Saw, and later Saw II, III, IV and V. He is portrayed by American actor Tobin Bell.
Jigsaw is introduced in the series as Jonathan Kramer,[1] a patient dying from an inoperable frontal lobe tumor that had developed from colon cancer.
In the series, Jigsaw usually creates deadly tests for his subjects, which are often a symbolic representation of what is seen as a flaw in the person's life. He claims that he is attempting to help his victims to appreciate their life by jumpstarting their survival instincts by placing them in life-threatening situations.

Traps
In the series, Jigsaw usually builds deadly traps for his subjects, which are often a symbolic representation of what what Jigsaw perceives as a flaw in the person's life. Jigsaw calls these tests "games", and tells the person the "rules" of the game usually by audio or video tape. The rules are tasks that the person must perform in order to pass the test and survive; however, the tasks often involve extreme self-mutilation (although there have been occasions where it is possible for the subject not to harm themselves if they are clever enough, such as the Hand Trap). On occasion, Jigsaw has used psychological torture for the subject's test.
Many of the games involve clocks, counting down timers or other measured time constraints provided to the victims. Jigsaw elaborated in Saw II his appreciation of "time", outlining the importance of savoring every moment. He also stated his belief that telling someone the time in which they may die would awaken an alertness for every moment of existence.
Jake Huntley wrote of the complexity of Jigsaw's character in the Irish Journal of Gothic and Horror Studies. Huntley described the intention behind Jigsaw's actions, and evaluated the extent to which they can be analyzed to fit into the philosophies associated with Deleuze, Darwin and Nietzsche:
The subject of one of Jigsaw's games is therefore always presented with an opportunity, the aim of which is to reinvigorate the potential of the subject, jump-start the survival instinct and instil a celebration or "savouring" of life. In Deleuzian terms, it is the potential of life that is at stake... It is this that gives Jigsaw's games their Deleuzian tone, the urgent revitalisation of life occasioning new experiences to be learnt and assimilated: such as the perverse, singular and aberrant situation of waking to find a man-trap secured around your neck. There is then the instruction to live or die, to make your choice, to survive the encounter with affect, or the affection-image... There is no thrill, sadistic or otherwise, in setting these games; they are throws of the die by the subjects, aleatoric opportunities... As Jigsaw makes clear to Detective Matthews during their conversation in Saw II, where Jigsaw's motivation and philosophy are most comprehensively explored, "I've never murdered anyone in my life. The decisions are up to them." Whilst it probably wouldn't stand up in court, he is at least correct in his usual, carefully literal sense. The decisions, the choices, the selection of a potential, are in the hands of the subjects of his games and he only intervenes in order to keep the game within its rules so a decision can be reached. The subjects are faced with a shocking choice that forces them to acknowledge what Deleuze identifies as the virtual – that is, the unacknowledged aspects of our experience with reality.
This, in effect, is the particular game that Jigsaw himself plays – one where the organism might be failing but the flow of desire succeeds and endures. Jigsaw might resort to discussing Darwin's "little trip to the Galapagos Islands" to provide a theoretical underpinning for his project and echo Nietzsche in talking of the will to survive, but this merely misdirects investigators and witnesses in the same way that the gruesome traps and freely-flowing gore earn him his unsettling serial-killer soubriquet. Jigsaw's games are designed to crack open the world of their respective players: the challenges are nearly always relevant to the subject's lifestyle in a symbolic or literal way, bringing them to (painful) self-awareness, prompting a reappraisal of their squandered potential.[11]
Jigsaw intends through these traps to force his victims to prove to him that they are "worthy" and "deserving" to continue living, and also for them to learn to abandon what he perceives to be their vices. Jigsaw often expressed a desire for his victims to succeed, but stressed that their fate was always in their own hands. The video- and audio-tape instructions for his games often echo this idea: "Live or die. Make your choice."