CUIDADO

Concessionaire in the UK, and I think the US, is the person granted the concession. Hence Grantor/Consessionaire. Concessionaire sometimes means grantor of the concession and consessionee the grantee.
See http://en.wikipedia.org/wiki/Concession_(contract)

EG. US - Concessionaires

We're looking for the best of the best in food vendors to support the 65,000 attendees we have each year. Many of our concessionaires have worked with us for multiple years and we are always excited for new possibilities. Check out the details below and find out how you can be a part of the celebration!
http://www.cityofallen.org/departments/parks_recreation/alle...

UK
Contract concessionaire: UK-Warrington: canteen and catering services
UK-Warrington: canteen and catering services
CONTRACT NOTICE
SECTION I: PUBLIC WORKS CONCESSIONAIRE
http://www.publictenders.net/tender/88065
These are the terms I use.
Concesionario = concessionaire
Concedente = grantor (of the concession)

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Note added at 5 hrs (2011-01-20 09:13:45 GMT)
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I have never ever seen concessionaire/concessionee in practice.

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Note added at 13 hrs (2011-01-20 17:35:23 GMT)
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In this context we are talking about something like

Benettonio granted me an exclusive concession to sell their red underwear range in the Solomon Islands.