I suspect that randomness of some sort is the only way. Without that, whatever the rules of the game, there is a way to somehow get a slim advantage. You can make the advantage small and the costs to try to gain it large, such that it isn’t cost effective to try, but as we’ve seen with HFT, it’s amazing how much people will spend to pick up pennies. Even a tiny gain, exploited frequently enough can be quite profitable.

Another is to reset the clock on the auction each change

> random delay

A Poison process. Just specify the expected value. E.g., if the expected value is 5 seconds and have gone some hours without an event, then the expected time is still 5 seconds.

E.g., like the time to some radio active delay and whatever its expected value to decay is.

Or even a fixed delay. Imagine trading with one month delay - You'd have to bid what you think the stock is actually worth, not what you think everyone else will think it's worth in five milliseconds. That's extreme, of course.