Discrete, discreet trading

One of the things I was concerned with many moons ago is the difference between the types of behaviours you can get in discrete and continuous time. Continuous functions are funky beyond belief, and the less you have to reason about them, generally the better. (For a sample of some of the pathologies, see this book.) Therefore I was particularly interested to read a suggestion by Michael Wellman on making equity trading safer (and, by disallowing order sniffing robots, more discreet) by making it, well, more discrete. Here's the idea: Wellman suggests

a discrete-time market mechanism (technically, a call market), where orders are received continuously but clear only at periodic intervals. The interval could be quite short--say, one second--or aggregate over longer times--five or ten seconds, or a minute. Orders accumulate over the interval, with no information about the order book available to any trading party. At the end of the period, the market clears at a uniform price, traders are notified, and the clearing price becomes public knowledge. Unmatched orders may expire or be retained at the discretion of the submitting traders.

This is really a nice idea. Real users would notice no difference between a market discretised in ten second blocks and a continuous one, but at a stroke bad high frequency trading would be eliminated. Add in a minimum (but low) bid/offer spread too, and the system becomes significantly more robust. The high frequency traders can no longer take your money off the table.