Japan uses a lottery system to prevent price gouging, which leaves a bad taste in peoples mouths when it's used to purchase something like tickets to a music venue, but with the way graphics card prices have been escalating I wonder if a side effect of this is that people who purchase tickets are less likely to re-sell them, and that this could reduce the amount of graphics card resellers.

Like, lets say that we stick with first-come-first-served. The people who can afford to wait outside for a week in advance of a new GPU coming out are also probably going to re-sell them, because the average person will install and use the thing until it breaks, giving it no other value than the initial cost, whereas a reseller could buy out the stock and make double what they spent.

Changing to a lottery system could reduce the final cost of the product if calculated correctly, and it would mean that instead of scalpers getting ahold of it first, everyone has an equal chance of getting it, and the majority of people don't intend to buy it for resale, meaning the majority of sales will be directly to the final customer. With resales becoming less viable a business strategy, less resales would occur, driving down the price of resales.

The question then would be, how much would a lottery need to cost in order to disincentivize resales. It'd need to be far too expensive to buy a huge quantity of tickets, at least in terms of making a profit. The cost to participate in the lottery would need to account for the amount of cards in stock, the amount scalpers are expected to aim for once they win, etc.

The next question would be, how would the lottery work. Do you buy once and then wait a few rounds until you win, or do you need to re-apply each time? While the second one would be better news for scalpers, it's still random chance, so they'd need to buy a high percentage of tickets in order to make it profitable, and so the ticket price can be used to negate that. Alternately, making the ticket price smaller but you have to purchase new ones each time would quickly bleed the energy out of any scalper organization, reducing the odds of losing since they wouldn't even participate without a guarantee to win.

The problem is that all lotteries can cause people with gambling addictions to take risks they can't afford, and so instead of dealing with scalpers people would be dealing with gamblers/hoarders.

Primarily, the reason for shortages will always be risk aversion. Companies can't afford to create millions of a product that may need to be recalled and replaced if there's any issues, or a product that doesn't sell as much as expected, not all on day one at least. It's not like a videogame that can be copied infinitely, you cannot scalp digital service games. Since risk is important to making efficient use of resources, this will be a problem until resource scarcity is solved once asteroid/space mining and manufacturing begins. Until then, we need tools that hurt scalpers more than they hurt consumers.