Recent studies suggest that the traditional determinants of housing wealth are insufficient to explain its current inequality levels. Thus, they argue that efforts should focus on understanding institutional factors. From the perspective of complex adaptive systems, institutions are more than the ‘the rules of the game’, they also consider the interaction protocols or the ‘algorithm’ through which agents engage in socioeconomic activities. By viewing markets as complex adaptive systems, I develop a model that allows estimating how much housing wealth inequality is attributable to the market institution. It combines virtues from two different modeling traditions: (1) the microeconomic foundations from overlapping-generation models and (2) the explicit interaction protocols of agent-based models. Overall, the model generates prices and housing inequality endogenously and from bottom-up; without needing to impose assumptions about the aggregate behavior of the market (such as market equilibrium). It accounts for economic and institutional factors that are important to housing consumption decisions (e.g., wages, consumption of goods, non-labor income, government transfers, taxes, etc.). I calibrate the model with the British Wealth and Assets Survey at the level of each individual household (i.e., ~25 million agents). By performing counter-factual simulations that control for data heterogeneity, I estimate that, in the United Kingdom, the decentralized protocol interaction of the housing market contributes with one to two thirds of the Gini coefficient. I perform policy experiments and compare the outcomes between an expansion in the housing stock, a sales tax, and an inheritance tax. The results raise concerns about the limitations of traditional policies and call for a careful re-examination of housing wealth inequality.