Who is primarily responsible for determining the market value of the home you want to buy?

there is no "individual" person or a central authority that dictates the market value of a home, instead, it is influenced by several market conditions and factors such as,

External characteristics: home condition, lot size, popularity of an architectural style, water or sewage systems, sidewalk, paved road and so on.

Internal characteristics: size and number of rooms, construction quality, appliance condition, heating type, energy efficiency and so on.

Supply and demand

Location