A mishap in the prize area of a Times Square arcade on Saturday night led to a fight between two men that ended when one pulled out a knife and stabbed the other to death, the police said.

The victim, Allen Stanford, 39, of Harlem, had been reaching for a prize on a high shelf at Dave & Buster’s when the item fell and might have struck a little girl who was with Jesse Armstrong, 41, the police said.

An argument between the two men escalated into a fist fight before Mr. Armstrong pulled out a knife and stabbed Mr. Stanford, according to the police.

Dave & Buster’s, a popular, family-friendly venue on West 42nd Street near Eighth Avenue that has attracted celebrities like Beyoncé and Drake, allows customers to exchange tickets won at arcade games for prizes like stuffed animals, candy, appliances and Sony PlayStations.

The prize at the center of the deadly dispute on Saturday night was said to be a drone, according to one person who was briefed on the matter.

Around 10:45 p.m., the police said, officers responded to a 911 call about an assault in progress and found Mr. Stanford at the scene with a stab wound to the chest. He was taken to St. Luke’s-Roosevelt Hospital, where he was pronounced dead, the police said.

Dave & Buster’s said in a statement: “We are fully cooperating with police in their investigation. Our thoughts and sympathies are with those affected by this terrible incident.”

Mr. Armstrong, who, according to the police, lives in the Morningside Heights neighborhood in Manhattan, was arrested on a murder charge after the stabbing. He was awaiting arraignment in criminal court in Manhattan on Sunday afternoon.

On Sunday afternoon, with the restaurant and arcade both open, a few dozen customers roamed a gaming area filled with blinking lights and bells and stocked with player consoles, high-definition video screens, old-fashioned mini basketball hoops and prize-claw machines.

Inside the prize store at the back corner, trinkets that could be paid for in tickets won in the arcade were hanging from spindles or sitting on high shelves: a colored fleece blanket for 1,850 tickets; a giant stuffed panda for 12,000; a brand-name kitchen mixer for 130,000.

After visiting Dave & Buster’s on Sunday, Kenya Woods of Manhattan walked out onto a busy 42nd Street with two relatives. Ms. Woods said she went in knowing that a stabbing had occurred there the night before.

“Whatever’s going to happen is going to happen; you have no control over that,” she said. “This is what it’s like in New York now, unfortunately. You can’t let it stop you from living your life.”

Susan C. Beachy contributed research.