I don't see a reason that "normal" investors would be at an arbitrage disadvantage if trading on an exchange that was discretized to, say, 100ms. Arbitrageurs would still have an incentive to keep the prices on the "slower" exchange in line with the "continuous" exchange's prices, trading at the discrete ticks to exploit price differences. So, price differences past an epsilon shouldn't persist for more than a few ticks, which is more than fast enough for most non-HFT investors, who don't typically make trading decisions with anything close to sub-second precision anyway.

I think a bigger question mark with my admittedly offhand proposal is whether discretizing might actually increase gaming opportunities, since the change could do non-obvious things to the strategy space. On the other hand, it might also remove existing market-gaming opportunities (which are fairly poorly understood, and axiomatically assumed not to exist by the idealized equilibrium analysis economists typically use). Alas, current game-theory solvers don't scale up anywhere close to well enough to give solid answers in either direction (real markets are a bit more complex than 4-participant games iterated over 10 timesteps...).

>I don't see a reason that "normal" investors would be at an arbitrage disadvantage if trading on an exchange that was discretized to, say, 100ms. Arbitrageurs would still have an incentive to keep the prices on the "slower" exchange in line with the "continuous" exchange's prices, trading at the discrete ticks to exploit price differences. So, price differences past an epsilon shouldn't persist for more than a few ticks, which is more than fast enough for most non-HFT investors, who don't typically make trading decisions with anything close to sub-second precision anyway.

Sure, but what you're missing is that the slow exchange's prices are always going to be worse. Not a lot worse - probably only a penny either way on some ticks, and zero on other ticks - but a little. So why would any investor with the choice ever choose to trade on the slow exchange rather than the continuous one?

"Worse" in what sense? Won't the prices deviate pretty randomly around the true price, sometimes behind a penny higher than the continuous exchange, and sometimes a penny lower, making it basically a wash?

No. If the discrete exchange makes it possible to withdraw an offer in between ticks, then the HFT guys would do that every tick - so you actually wouldn't get a price (or you'd get a very wide spread), and it would basically fail to be an exchange. So let's assume any order you have on the book stays there until the next tick's auction. In that case the HFTers are going to give a much higher spread, because if new information comes in at 3.2s and the stock is suddenly worth more than it was at 3s, but they can't withdraw their sell order until 4s, then obviously they lose money. So occasionally you'd get a better price on the discrete exchange (when the market moves further than the spread in the space of one tick) - but the HFTers would be terrified of this situation, and make their spreads wide enough that they think it's impossible. So 99% of the time, you'd get a worse price.