Shares of GameStop, the world’s largest video-game retailer, rose the most in over four years after Sony said its coming PlayStation 4 will allow unlimited used-game sales.Shares advanced 7.8 percent to $37.72 at the close of trading, the largest jump since March 2009, making GameStop the biggest gainer in the Standard & Poor’s 500 index. The Grapevine-based retailer has added 50 percent this year, while the S&P has advanced 14 percent.GameStop stock has fluctuated this year on speculation about potential restrictions on used-game sales in the new generation of consoles. Sony’s announcement Monday, after Microsoft’s decision last week to allow resales of used games on the coming Xbox One, means “status quo,” according to Peter Moore, chief operating officer of Electronic Arts.“A lot of people thought Microsoft or Sony would put up a wall,” Moore said in an interview with Bloomberg Television. “That’s not the case.”Sony said Monday that the PS4 won’t put any limits on consumers’ ability to freely share and resell used games.Microsoft, which announced Monday that the Xbox One will debut in November for $499, said last week that it will let game publishers decide whether to allow resales of titles for the console to selected retailers. Games can be given to friends only once, and shared with restrictions.GameStop helps spur new-game sales because customers trade in older titles to buy newer ones, GameStop CEO Julian Raines told Bloomberg Television. He said GameStop will be the dominant retailer for Xbox One in all the markets where it has stores.“We’ll see a rising tide as people spend more time in all forms of gaming,” Raines said.GameStop has reported lower or unchanged revenue in the last six quarters as a consumer switch to mobile devices hurt sales of traditional video games. Preowned games, which GameStop customers trade for new versions, were 31 percent of first-quarter revenue; new ones represented more than 37 percent.Sony’s new PlayStation is the company’s first new console in seven years and will cost $399, or 20 percent less than the Xbox One.Nintendo’s Wii U player, introduced in November and priced at about $300, has sold below expectations. On Tuesday, the company announced new titles coming this year and next, including some of its biggest franchises: Super Mario, Donkey Kong, Zelda and Super Smash Bros.