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Sprint’s new unlimited wireless plan, announced last week after its $21.6 billion acquisition by Japan’s SoftBank, did not deliver the aggressive price cuts that some analysts had expected.

But cheaper plans could be coming.

In a phone interview, Masayoshi Son, SoftBank’s chief executive, hinted that further price cuts could be in the works as the company invests to upgrade Sprint, America’s No. 3 wireless carrier.

“We will be aggressive in technology, price packages, services on every front,” Mr. Son said from California on Wednesday. “At the same time, we will improve the network to be the world’s best,” he said.

SoftBank, the Tokyo-based Internet and mobile communications giant, has a reputation in Japan for undercutting rivals on price to gain market share. Mr. Son has been behind a sharp decline in prices for broadband and cellphone services in Japan.

Expectations are high that Mr. Son will bring that strategy to Sprint, which has struggled with subscriber defections for years and that Mr. Son will inject healthy dose of competition to America’s mobile industry.

But Sprint’s price cuts have not been particularly groundbreaking, and executives have said the cuts were in the works before the SoftBank acquisition.

Under Sprint’s new wireless plan, customers pay $80 a month for unlimited data, texting and calling, down from the $110 Sprint had charged for a similar pricing.

“This is not the ‘magic behind the black curtain’ moment that many were waiting for with SoftBank,” Jennifer M. Fritzsche, senior analyst at Wells Fargo Securities, wrote in a research note on July 12.

Sprint remains under pressure from T-Mobile USA, the No. 4 wireless network, which has been offering a $70 package for unlimited talk, text and data from earlier this year.

Verizon, the industry leader, offers a shared data plan with unlimited talk and text messages for $90 a month, while AT&T, the No. 2 network, has a similar plan for $85.

Mr. Son has said that he planned to invest $16 billion in Sprint over the next two years to shake off competition from T-Mobile while also closing the gap with Verizon and AT&T.

Most of that investment will be spent on base stations for Sprint’s advanced LTE network, he told the Nikkei newspaper earlier this month.

And if SoftBank’s past antics in Japan are a clue, Mr. Son could also start driving down prices.