DoorDash held talks to buy Instacart over the past two months, say people familiar with the situation, for a price that likely would have been between $40 billion and $50 billion. It would have combined a leading restaurant-delivery service with one of the leading grocery-delivery services.

But the talks fell apart in recent weeks, at least partly due to questions about whether a combination could get approval from antitrust regulators, which, under the Biden administration, are taking a hard line toward most mergers. The fact that the companies talked at all, though, shows how they’re looking for ways to strengthen their businesses, countering growing competition and a slowdown in growth sparked by the end of pandemic lockdowns.