Federal regulators have vowed to investigate a growing trend in video games that analysts say could soon become a $50 billion industry but that has drawn fire from critics who compare the practice to gambling.

Senior officials at the Federal Trade Commission, America’s top consumer watchdog, said Tuesday that they will look more closely at loot boxes — the bundles of digital goods offered to players, often for a fee, that contain random assortments of in-game clothing, abilities or other rewards.

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