Economically affordable housing (EAH) system is aimed to resolve the housing problem for people without housing or poorly-housed families. However, driven by the economic benefit, increasing homebuyers ineligible to purchase EAH provide fake materials to acquire EAH, which makes EAH system deviate from its original aim. In the paper, we put forth the critical value of surveillance intensity by the government through the game analysis on the government and the fraudulent purchasers and conclude that the fraudulent purchase can be effectively controlled as long as the critical value is satisfied. Based on this, punishment measures and intensities for the fraudulent purchase are surveyed and quantified, and thus come up with the various supervision and surveillance intensities needed by the government for each punishment measure. This provides a theoretical basis and quantitative standard for the government to formulate an effective management system.