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Matching markets (people have different preferences for different goods (A…

- - - - Constricted set: S>N(S) #buyers > #preferred_sellers
      - The only reason that there's no perfect kaching is the existence of a constricted set
- - - - A generalization of the perfect matching problem
    - - for a set of prices there's a ...
        
        BIPARTITE GRAPH OF PREFERRED SELLERS
        
        For a set of prices, there's a network os preferred sellers
      - Market-clearing prices: one buyer for one item (there may be ties)
        
        Theorems
        
        Theorem: the perfect matching has the maximum total valuation
        
        Demonstration by Egerváry (1916)
        
        Theorem: for ANY set pf prices there's ALWAYS a setof market-clearing prices
        
        The preffered-seller graph has a perfect matching
        
        In a single-item auction, the market clearing price is the second highest valuation (the item is sold to the buyer with the highest valuation)
        
        The algorithm to get market-clearing prices using a generalization of an ascending price auction