Wells Fargo & Co., lagging behind its rivals in mobile-banking prowess, is turning to an unlikely source for advice: the video-game industry.

The lender bought a small stake in Context360 Inc., a startup that makes behavior-predicting technology used by game makers to retain mobile players. For Wells Fargo, similar technology could help it pitch car loans on Saturday mornings when customers visit dealerships, for example, or block a suspicious credit card transaction, according to Stephen Burke, Context360′s chief operating officer.