Quincy Sharp is the warden of Arkham Asylum. He is captured when the Joker breaks free and turns the asylum into his personal playpen.
Through various deciphered messages in the Asylum, you learn that Sharp has a tendency to act violently towards the inmates, and believes they should be killed in order to save their souls and protect innocents. He also shows the inability to kill the Joker when he hesitates after holding him up with a knife, allowing The Joker to take the knife and hold him hostage.
Batman: Arkham Asylum
Sharp meets Batman and the Joker at the entrance to the asylum, ordering a phalanx of guards to assist Batman in escorting the Clown Prince of Crime to Intensive Treatment. Upon hearing of the Joker’s escape, Sharp headed down to investigate where he was captured by Harley Quinn. Following Batman’s incapacitation of Victor Zsasz, Quinn contacted Batman via closed-circuit television and flaunted the bound and gagged Sharp.
After Dr. Young’s death at the hands of a booby–trapped safe in Sharp’s office, Batman is briefly stunned and confronted by Quinn in person. Quinn, having dragged Sharp along, removed the duct tape from the warden’s mouth long enough to hit him over the head with his own walking stick. Before Batman could recover, Quinn fled with Sharp in tow. Batman used the DNA from Sharp’s cane to calibrate his visor and track the imprisoned warden to the cell block.
Batman tracked Quinn and Sharp to the Security Control Room, where the warden had been stashed. Batman was able to free Sharp and obtain the security codes that would allow him to bypass the many locked doors remaining in Arkham. The Dark Knight ordered Sharp to barricade himself in the control room and left in pursuit of Quinn.
Once Batman succeeded in locating all 23 of the hidden “Chronicle of Arkham,” however, Warden Sharp’s true motives are revealed. Sharp suffered from an acute form of schizophrenia that manifested itself via an alternate personality. Believing himself to be the reincarnated spirit of the Asylum’s founder, Amadeus Arkham, Sharp harbored an intense hatred for all the prisoners under his care. Sharp began to believe that the only true cure for insanity was death.
Upon learning the truth, Batman returned to the Security Control Room to confront Sharp, only to find the warden gone. A final, hand-written chronicle left specifically for The Dark Knight implored whoever read it to continue Sharp’s work.
After players complete the main story line, they can return to Warden Sharp's office where there is now a destructible wall. Through the wall is a secret room, sparsely furnished, but it contains a map indicating the possible location of another Arkham Asylum, this time within Gotham City itself.
The location of the secret room was given away by the development team in a podcast, recorded for the release of the Game Of The Year Edition of Batman: Arkham Asylum.
Batman: Arkham City
In Arkham City Warden Sharp is now Mayor Sharp. In the time between the two games he got elected mayor AND convinced the city to section off part of Gotham and turn it into Arkham City the prison. Late in the game (SPOILERS) he gets arrested and thrown into the prison by Hugo Strange. Batman then had to rescue Sharp from various thugs who wanted revenge.