I don't think uber isn't a winner take all market. 1. uber sets pricing. 2. uber is a 2 sided market not an n sided market like a communication platform. The premise that more drivers equals less wait time and lower prices is partial wrong. more drivers waiting on fares will decrease wait time. I predict a second player that offers higher wages per trip would entice drivers to wait longer for fairs offering much faster times to customers.
also, if you have a grid with a 16x16 with a point in the middle it would need to travel ~4*1.4 to reach the furthest point on the grid. in order to 1/2 the time it takes you need split into 4 quadrants and add 3 more cars. if you want to half the time again your looking at 17 cars. so to go from 10 minutes down to 5 minutes down to 2.5 minutes it takes ~4 times as many drivers each half. rough calculation. if anyone would like to add a better approximation I love to hear it.
There is an important lesson to be learned from each generation of digital disruption. Like Airbnb, the leading search engine Google, leading social network Facebook, and leading video platform YouTube have limited competition, making platforms a high-stakes, winner-takes-all game. Every company facing digital transformation runs the risk of losing relevance and becoming redundant in a future consolidated by platforms.