Matching Principle for Uber
https://marketplace.uber.com/matching
This is an article published by Uber on their website to explain how the company matches their drivers with their passengers. Uber’s network seems quite simple, but considering the fact that there are millions of users online everyday globally, how to match in a way that compromises are made to maximize the overall social benefits remains a challenge. For the drivers, they want to minimize the amount of time between the actual rides (time without rides or time spent on their way to pick up the next passenger) so that they can make the most money in a day, while the riders obviously want to wait as shortly as possible. Therefore, for both drivers and riders, the shorter the time that drivers spent to pick up the passenger, the higher the payoff for both parties. 
Figure 1
As shown in figure 1 above, when there is only one person requesting a ride, Uber can simply match the closest driver to that rider. However, as shown in figure 2 and 3 below, when multiple requests happen at the same time, there will be multiple perfect matches, and some compromises need to be made in order to maximize total social welfare, least wait time, in this case. As illustrated in figure 2, if Uber still matches rider #1 with the driver who is the closest to him (2 mins), rider #2 will have to wait for 9 mins for the other car. The total wait time will be 11 minutes. On the other hand, as shown in figure 3, if Uber matches rider #2 with the car that is closer to rider #1, and matches rider #1 with the other driver who are relatively farther, but much closer to rider #1 than rider #2. Both riders will need to wait for 4 minutes, and the total wait time is 8 minutes, which is less than 11 minutes and more ideal for the society as a whole. 
Figure 2
Figure 3
This is also why there is surged price during rush hours. In the example above, both riders would want to be picked up by the top left driver. Although in reality users do not know drivers’ availability, increased price for rides will reallocate demands for cars nearby and thus clear the market. Uber’s matching algorithm perfectly demonstrates concepts we went over in class this week including perfect matching and maximizing social welfare.