SoftBank Group Corp.’s bid to take a stake of as much as $10 billion in Uber Technologies Inc. is a high-stakes bet on the future of the car industry.

SoftBank’s billionaire founder, Masayoshi Son, aims to build a global network of ride-hailing companies with a lock on important markets that in the next 20 or 30 years could control fleets of vehicles and help dictate how people move around, say people briefed on his strategy.

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