We express Gp=(X U Y, E) is the preffered graph where ij in E if j is preferred seller of X=buyers, Y=sellers
--> A vector of prices p is market clearing if Gp has a perfect matching( generally, "Clearing means no excess demand or supply).
ALGORITHM - Start with prices p=(0,0,...,0) while Gp does not have a PM( perfect matching) Let A is a subset of X such that |N(A)| < |A|
For each j∈ N(A), Pj∈Pj +1
If Pmin > 0 then subtract Pmin from all prices [ pmin is matched at 0]
The algorithm terminates.
There is also a theorm which states: If p is a market clearning price vector then $m^p$ (a PM in Gp) is a maximum valued matching,
Using this information find Find a set of market clearing prices for the valuations below, by running the algorithm. The buyers are A,B,C,D.
I am not sure on how to run the algorithm. I have a similar question on my midterm tomorrow so any help will he appreciated.