Follow on to ticket analysis

There were some things I didn't make explicit, and I wasn't always clear with my terms. Re-posting this here to try to fix some of that.

1. I was working in demanded units, but I was sloppy and spoke of this demand as if it came from actual people in a 1:1 ratio. This is not what I meant to express. For example, the 91,000 tickets demanded by veterans if we assume scalpers have 5,000 tickets is not saying there is demand from 91,000 burners. It could be 30,000 burners asking for a little more then 3 tickets each. But were this the case, we'd all have more tickets. See point 4.
   
   
2. As far as tickets per bid, and bids per person, this is why I worked in units of tickets demanded: A ticket is directly convertible to one participant. But one potential participant could generate many bids, and each bid can be for one or two tickets. But since we have reasonable ideas about participant numbers and ticket numbers, working in these units removes unnecessary complexity, keeps the problem rooted in available facts, and avoids inserting unnecessary assumption points (how many tickets per bid? how many bids per participant?).
   
   
3. This is also done to shine a light on the demand amplifying impact of the lottery system: The structure of the sale makes participants amplify the demand signal they send to the market ("If I want two tickets and I have a 50% chance of being successful, I should bid for 4, because I'll probably get 2"). So the game, when played out, says everyone should increase their bids to infinity, as long as they believe in no liquidity risk ("But if I bid for 8, my odds of getting two go up, and if I have extras I'll just sell them. Maybe I should bid for 10. No, 12...").
   
   
4. If everyone amplifies their bid by the same factor, and if demand and supply were truly close to equilibrium, then everyone should get the number of tickets they need (50,000 people bidding for 50,000 tickets all bid for 5 tickets, each has a 1 in 5 chance of success, and on average, everyone gets one ticket. If they all bid for 6, they have a 1 in 6 chance of success. No shortage.). As this seems not to be the case, (and far from it), then either demand greatly outstrips supply (oh the places we all want to go!), or some participants scaled up their demand by a factor orders of magnitude in excess of the average participant (scalpers...?), or some combination of both.
   
   
5. My conclusion is that, while stated demand may have been amplified by the structure of the market (game), it doesn't seem to explain all the observable evidence, and so I have to conclude that scalpers were present. I reject my (null hypothesis) "weak" assumption that there was only tiny scalper activity.
   
   
6. One area that would be interesting to explore is assessing the outcome via market simulation. Determine the proportion of [good burners who bid for only what they need; scared burners who bid for more than what they need; virgins; scalpers] that produces an outcome consistent with the results. I'd need some time and help to go down that road. But possibly a good exercise for testing future ticket distribution solutions.