Is anyone familiar with 'equilibrium martingale condition'. I have come across this term in a number of market microstructure papers I have read but still don't comprehend what it means.

It is impossible to answer without knowing the specific context in which the quote occurs.But broadly speaking, if you build a model in which a stock may go up to SU with probability p or down to SD with probability (1-p) then the 'equilibrium martingale condition' says that SU, SD, p in your model must be chosen such that S0 = p*SU +(1-p)*SD where S0 is the current price of the stock. A model that did not satisfy this condition would be flawed in that it would be biased toward one side of the market (buyers or selllers). [added 4:59]:The French word martingale translates into English as: "the expected price in the future is equal to the price now"