I would like to know more about the economics of ticket scalping - how
ticket scalpers operate and how to get the best price from them.  More
specifically, would I be able to buy tickets at a steeply discounted
price if I wait outside the stadium/arena until after the event has
already begun, and then approach them to make an offer?  Do they
always sell all their tickets before "kickoff"?  Or do
they usually have a surplus of tickets leftover for which they have to
"eat" the cost because they can't sell them at all (and ideally would
be willing to sell them at a price below face value)?

Sure, ticket scalping is pure free market, the price is what a willing
buyer and a willing seller agree on, and of course, the scalper is
going to want to unload any tickets after kickoff, but he knows the
market better than you, and he may consider it a bad practice to
undercut the price if he is ahead on his portfolio; it just invites
potential customers to wait till the national anthem has been sung.
Scalping is also illegal in some areas.  A couple of months ago there
was a question about this.  When the crowd is gone, selling tickets
outside the stadium is more obvious.
And then there is the problem of conterfeit tickets ...