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We propose a general non-linear order book model that is built from theindividual behaviours of the agents. Our framework encompasses Markovian andHawkes based models. Under mild assumptions, we prove original results on theergodicity and diffusivity of such system. Then we provide closed form formulasfor various quantities of interest: stationary distribution of the best bid andask quantities, spread, liquidity fluctuations and price volatility. Theseformulas are expressed in terms of individual order flows of marketparticipants. Our approach enables us to establish a ranking methodology forthe market makers with respect to the quality of their trading.

From asymptotic properties of general point processes to the ranking of financial agents