Nash Equilibrium in Order Books

Nash Equilibrium in order books occurs when no trader has an incentive to deviate from their current buy or sell limit order given the orders placed by all other market participants. In the context of market microstructure, this represents a state where the spread between bid and ask prices is optimized based on the risk and liquidity preferences of all actors.

If a participant were to adjust their price, they would either reduce their probability of execution or receive a worse price, thereby decreasing their expected utility. This concept explains why order books often exhibit specific depth and density patterns during periods of relative market calm.

It assumes all participants are rational and possess information about the current state of the book. When market conditions change, the equilibrium shifts, leading to price discovery through continuous order adjustment.