I've checked to see how many fares Arriva have in the same areas that GNE operate in. There are more wholly outside of the GNE area, for the sake of comparison I haven't added them.
Single zones

• Bishop Auckland
  
• County Durham
  
• Durham City & Brandon
  
• Durham District
  
• Middlesbrough (borough and Stockton High Street)
  
• Tees Valley (Darlington through Staithes)
  
• Teesside (Stockton & Middlesbrough boroughs)
  

Network

• North East Regionwide (Berwick through Scarborough)
  

Northumberland + Tyne & Wear (formerly Triple)

• One Zone (Ashington, Blyth, Tyne & Wear, Tyne Valley)
  
• Two Zones (combine with any adjacent zone)
  
• All Zones
  

East Durham

• One Zone (Sunderland & Seaham, Peterlee)
  
• All Zones
  

Routesaver

• Coastliner (306/308 Blyth/Whitley Bay to Newcastle)
  
• 6 (Framwellgate Moor to West Auckland)
  
• X12 (Durham Bus Station to Newcastle)
  

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After looking through all the fares, there are some that could be changed...

• The Killingworth and Quorum routesavers appear to be the same, merge into one ticket.
  
• Morpeth Zone extended to Rothbury/Thropton, renamed Morpeth & Country Zone.
  
• Ashington Zone extended to Amble, renamed Ashington & Amble Zone.
  
• Rothbury and Morpeth routesavers replaced with NTW ticketing (Morpeth-Newcastle would be all zones).
  
• County Durham and Durham District tickets could be merged.
  
• Introduction of an Alnwick Routesaver (cheaper than NE Regionwide for Alnwick-Newcastle commuters, ideally allowing travel across all NTW zones) and an Alnwick & Amble area ticket.