Matching Markets and Ticket Sales — The Return of Brady
One thing that sports fans are all too familiar with are high ticket prices. Watching sports in person is never an inexpensive endeavor, especially when it comes to especially high-profile games. Unless you are a season ticket holder or buy tickets well in advance, getting tickets to an important match-up can be extremely expensive, if not nearly impossible. At the start of this season, the New England Patriots’ quarterback Tom Brady served a 4-game suspension for his alleged involvement in the “Deflategate” scandal. A beloved figure in sports and often referred to as the “King of New England”, Brady’s suspension was highly controversial and widely publicized by the media. The Patriots’ sixth game of the season marked Brady’s return to Gillette Stadium and resale ticket prices skyrocketed as thousands of fans clamored for seats for Brady’s first home game of the season.
The high demand and average ticket price of about $550 made this one of the most anticipating home games ever for the Patriots. With so many sports fans vying for tickets, it was inevitable that the limited number of tickets being resold would command high prices. There were many more potential buyers than available tickets being sold, leading to sellers being able to charge high prices and sell only to those buyers willing to pay the price. Each buyer has their own willingness to pay for different tickets, and in order to create perfect matching and ensure that all tickets were purchased there must be market clearing prices. This can be shown graphically by adding enough phantom items worth $0 to a bipartite graph and raising prices until there is no longer a constricted set and each buyer is matched with a ticket, even if these tickets are not real. This results in perfect matching between buyers and sellers. Each buyer has different valuations for different seat locations, and sellers are able to increase prices on seats that are in high demand until only the buyers that have the highest willingness to pay for the tickets ultimately purchase them and buyers matched with phantom items receive nothing. Thus games in which there is high demand always result in having the highest prices, and only the fans willing to pay a premium are able to secure seats.
Source: http://www.usatoday.com/story/sports/nfl/patriots/2016/10/14/tom-brady-tickets-gillette-stadium-new-england/92052936/