Pittsburgh’s mayor believes his city would have won $50 million in Smart City funding instead of Columbus – if only it had buy-in from Uber Technologies Inc.

The San Francisco-based ride-sharing company has built a large presence in Pittsburgh since 2015, including committing to a $1 billion Advanced Technologies Center and to test out its self-driving vehicle fleet on city roads.

But Uber wouldn’t work with Pittsburgh as the city put together its federal Smart City Challenge application –…