For quite a while T-Mobile (NASDAQ:TMUS) and Sprint (NYSE:S) avoided criticizing each other or even targeting the other's customers in favor of going after industry leaders AT&T and Verizon.

That changed quite dramatically in August 2014 when the two companies ended merger talks and Sprint replaced mild-mannered CEO Dan Hesse with the bolder Marcelo Claure. When that happened, T-Mobile CEO John Legere set his sights on surpassing Sprint as the No. 3 carrier (which his company did not long after). In verbal barbs and promotional offers both companies starting aiming at each other.

The gloves came off, but T-Mobile has been better at fighting than Sprint. 

How goes the battle?
In a broad sense, Sprint has become a sort of T-Mobile Lite trying to go against industry norms without the success or panache Legere has managed. Claure's company has also tried to copy Legere's by targeting its rivals specifically with promotions. The fourth-place carrier, for example, recently took a shot at the new No. 3 by reintroducing its "cut your bill in half" offer -- which does not actually do that -- and extending it to T-Mobile customers (last year's version of it only applied to people jumping from AT&T and Verizon).

Legere clearly did not like that, because he responded with an offer to give Sprint customers $200 to switch to T-Mobile. The deal does not require customers turn in a device and it's on top of the Un-carrier being willing to pay any early termination fees the switcher may incur (which would require turning in a device).

This is Legere firing a shot directly at Sprint in an attempt to keep the struggling carrier from turning its momentum around.

"I cannot think of any wireless customers in more desperate need of some holiday cheer than those Sprint customers still hanging on over there," said Legere in a press release.

Legere never skips an opportunity to take a shot at Sprint. Source: John Legere's Twitter feed. 

What is T-Mobile doing?
It's a bribe. However you look at it T-Mobile is putting cash on the table to get Sprint customers to switch. The company explained the offer in its press release:

Just switch any Sprint number – including postpaid, prepaid, Boost and Virgin Mobile – over to a T-Mobile Simple Choice postpaid plan...and you'll automatically get a $200 credit on your bill.  That's $200 multiplied by as many lines as you switch.  For a family of four, that could mean $800 extra, and for a business with 10 employees, we're talking about a $2,000 credit!

That's a very simple proposition that might make people who were intrigued by T-Mobile -- but not up for the hassle of switching -- pull the trigger. It's a bold move, but also a risky one because the new users only have to stay until the credit has been processed. There is no contract or commitment beyond that.

Does this offer make sense?
While Legere's actions sometimes seem like he is spending too much money to acquire customers, his company has been growing rapidly for over the past two years. Sprint has tried to copy some of its Un-carrier initiatives, but hasn't created a customer identity the way T-Mobile has.

Sprint has received unwavering support from principle owner SoftBank, but it's also in the midst of cutting $2 billion from its 2016 budget, reported Reuters. The company said the cuts will come from labor costs, network operating expenses, information technology, and administrative expenses, according to the news service. Those are tough areas to rein in expenses on while also trying to add customers.

Sprint's cuts create an opportunity for T-Mobile to be even more aggressive. Its majority shareholder Deutsche Telekom AG has supported Legere in playing a long game. Offering Sprint customers $200 to switch is a bet that its customers will not just join T-Mobile but stay for the long term.

Will it work?
While paying $200 plus ETFs inc some cases for new customers makes the eventual month when T-Mobile makes money on those users well into the future. That may have been a dicey proposition in the past for T-Mobile, but its improved network and high levels of customer satisfaction make a long-term strategy sensible for Legere and company.

T-Mobile topped the 2014 J.D. Power U.S. Wireless Customer Care Full-Service Performance Study Volume 2.  In addition, its MetroPCS brand topped the J.D. Power survey for non-contract providers.

Essentially Legere is betting that if his company spends an extra $200 per Sprint customer it acquires, it will hold them long enough to make money. That's a reasonable assumption when you consider that Sprint and T-Mobile generally offer lower prices than AT&T and Verizon. That means the Un-carrier likely won't lose any acquired customers as long as it delivers quality service at a low price.

Given T-Mobile's improving network and the relationship it creates with its customers, that should be the case. As long as Legere continues to bridge the gap between his network and his rivals' (and the most recent RootMetrics report shows the carrier is doing that), T-Mobile should be able to hold onto any Sprint customers it adds.

This is a bold offer, but it's actually a smart investment in getting Sprint users -- the customers most likely to stay T-Mobile customers -- to make the switch.

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Daniel Kline has no position in any stocks mentioned. He should have waited a couple more months to switch from Sprint to T-Mobile. The Motley Fool recommends Verizon Communications. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.