“An unlimited offer is dangerous,” said Roger Entner, an analyst at Recon Analytics LLC. “If they sign up a lot of people, it will congest the network, and they run the risk of people saying ‘the network sucks’.” Verizon’s ability to retain its reputation as the nation’s premium network provider will be critical as pricing wars escalate with rivals T-Mobile US Inc. , whose Chief Executive Officer John Legere took credit last month for dragging the phone giant “kicking and screaming into unlimited.”