How does the Uber's pricing model work? I'm working on a paper on the sharing economy, and in particular on its economic implications.

I am aware of the surge pricing model that Uber adopts, and of how it works. But I'm wondering on what criteria and how Uber estimates the base fares of each city.

I would like, ultimately, to understand whether and why this artificial pricing model is better than the "natural" pricing models of other peer-to-peer services (e.g. AirBnB), that allow the users to set their own rates.
It is important to distinguish between optimal pricing from Uber's perspective and optimal pricing from an efficiency standpoint. If Uber was the only company matching drivers and customers, it would adopt a monopoly pricing strategy on selling rides to consumers and buying rides from drivers. These rates may be very far from the efficient rates. It is therefore important to state what you mean by a "better" pricing model.

From the perspective of Uber/Airbnb, profit maximizing pricing strategies may differ because of many reasons. AirBnB is in a business where the quality of a service can vary greatly and is often unobserved to them. Uber in contrast matches customers with services that have little to no variation in quality (speed, safety), which are fairly well observable due to their GPS data. But even depending on expected company growth may lead the two companies to have optimal pricing strategies closer or further from efficient prices. Finally, the competition in each city may be very different for Uber, since cab rates are fixed by a central planner. The competition of AirBnB usually has decentralized pricing except where a hotel chain has a local monopoly.

Even from an efficiency standpoint, there may be large advantages from a centralized pricing strategy in the market for rides. Most urban areas have fixed cab ride rates to increase transparency. Anybody can get into a cab without worrying about being charged an unexpectedly high amount. This can greatly enhance market outcomes.