[But for me is quiet clear (probably i'm wrong...) that in the game of buy and sell it's important the history of the price.In one sense pretty much all models of MMs use some sort of "history". It can be a subtle point.Take volatility, in >90% of what you read about the standard models, volatility is assumed to be an instantaneous quantity, ie measurable at a point, and models like Black-Scholes assume you know what it is going to be. But of course neither are true.MM models frequently use volatility to predict rational behaviour, since it is intuitive that bid-offer spreads are driven at least in part by the volatility.Forward volatility is usually taken some function of recent history.However "history" shows little predictive power, thus although individuals may use it to determine trades, the actual price is usually pretty independant of history. This is not always intuitive. (do we agree that many people buy and sell because of the history of a particular asset?)Some people do.However, it is frequently the case that the reason people can make money from an "efficient" market is that people can act stupidly even if it is a rational view. That i expect is an amplification of bad events, (catastrophe and bifurcation theory) due to the (small) delay efect.Dealys are something I care about actually, since my job involves prices moving physically around the market.You also need to look at relativity here, yes really. Prices do not reach everyone at the "same time", they are not processed at the same speed, and often it is the case that the person who reacts first get the whole amount available at that price.By the way, Did your model work, I mean, do you get something like a log-normal random walk for a stok? I'm very interested on it.It could be made to do that, though it was harder than you might expect. However to get any sort of LNRW I had to alter it with the goal of making it that way, rather than just toss in parameters. If LNRWs were only to be found in a a few markets, then I'd be tempted to assert that LNRW was some sort of coincidence, but we observe that most markets are at least mildly LNRW.The mechanism I belive can be seen if you imagine a market that was not LNRW.Perhaps this might be because one common type of customer had to buy at a certain time.However, people would notice this effect, and two things would happen.Firstly, those who didn't have to sell then would avoid doing so, since they'd get inferior prices.MMs would learn and thus take positions ahead of time to exploit it. This would of course result in rational bubbles.Doesn't have to be t ime driven , if an effect is driven by any visible signal then people will exploit it, and by doing so erode it almost away. This is pretty much a mainstream view of why the efficient market hypothesis works (mostly).