## The Game behind Parking Auctions

http://www.wired.com/autopia/2011/08/app-lets-drivers-auction-public-parking-spaces/

Recently a new app has been launched for iPhone users to auction parking spaces using their cell phones. Although still beta-testing the app, the developers believed that it has the potential to gain a global market in the near future. The app is currently being used primarily on Manhattan’s Upper West Side, and here’s how it works: since the parking spaces are not for sale, what the drivers selling is actually the information of when, exactly, a space would be available. Despite the fact that the transactions are not yet made real “auctions”—there are no bidding going on besides the sale, people’s behavior of buying or not buying the new deal can be explained by the underlying game theory.

In class we talked about game theory and its application in real world stories. Here in the parking auction, each buyer is a player in the “game”, and he or she can choose to buy a space, or to bet on luck.

To interpret this game by a matrix, we set the following rules: each driver who is looking for a parking space is a player, the two strategies that the players can choose are either to buy a parking space through the app, or not to buy it—find a spot themselves. The value of getting a parking space quickly is 30, but by quickly we mean the player necessarily buys the space using the app, which has a cost of 10; yet not finding a space in time, denoting not to use the app and with a low chance of luck in a high traffic area, the time wasted costs 15. Since this game involves multiple players (though we only take two players into consideration, the rest of the game works the same), if someone buys a space, then the other drivers who are randomly looking for spots themselves has an even lower chance to get a free spot, thus further increase the cost of time wasted to 25. However, if two drivers make a purchase at the same time, they both get a lower value out of their transaction—that is, they only get 20 because space available for parking decreases. As we put these values into the payoff matrix, we see that if two drivers both buy a space, their payoff would be (5,5), which is 20-15. And if they both do not buy, the payoffs are (-15, -15). If one buys and the other does not, the player who buys it gets 30-15=15 and whoever not buying it gets -25. A payoff matrix can be constructed as the following:

This game is very similar to a prisoner’s dilemma game, in which a player gets the highest payoff confessing while the other player does not confess. In this parking auction game, a player’s best response is always to buy the parking space no matter what the other player does. Therefore, similar to the prisoner’s dilemma which can be considered a subtle design to make the prisoners believe (and it truly is) their dominant strategy is to confess, the parking auction game shows the drivers that the best way to go is to buy a space no matter what others are doing. The Nash Equilibrium in the game is therefore the upper left cell, which corresponds to both players buying. A game theory analysis well described how the parking auction app will be profitable as expected if drivers would follow what the game shows.