Recognize the sponsers contribution by a small discount in the purchase rate
You are missing the point, sponsors get tickets, it's nothing to do with how much they pay for them (and frankly it's part of the negotiation how much they sponsor vs number of tickets, so your comment is a little silly).
They give them away (like all those "buy this item and be entered in a lottery for a ticket).
It's the people who receive the tickets then not using them that is the "issue", they can't sell them or even give them away, so they go in the bin, rather than on ebay.
And the solution is no "well then don't give sponsors tickets", because then you get less sponsors and more taxpayer money has to be coughed up.