no. business school teaches you that you can compete on price (cost strategy), or on value (differentiation strategy).
if you compete on price, you’re betting that you are, or will be, the most efficient provider in the market (e.g., walmart and its supply chain dominance). it’s completely viable/acceptable to compete on price. what you don’t ever want to do is price on cost, rather than on value provided.
you can also compete on being better in many other dimensions, which is lumped into the broad differentiation strategy category. you are then betting that you are better on your dimension and that customers really value that dimension (more than price).
A classic example (presented to my MBA class) was the two adjacent pizza parlors in NYC competing on price and driving the selling price of a pizza down to less than a dollar, whilst a shop a block away and around a corner was able to keep normal pricing.
but you also compete on price in the marketplace--not so much as to ignore your costs, as you note, since negative margins generally don't lead to viable businesses, but price competition nonetheless.
your example is the simplest game-theoretic version of price competition, which is more of a teaching model than a practical application.
(dynamic) price discrimination and other marketing tactics are typically employed to ensure positive margins even as you compete on price in the marketplace (e.g., airline seats).
no, you should compete on price if you are the low cost producer, as my neighbor comment notes. monopolists frequently are the low cost producer because of economies of scale, scope, etc.
another "compete on price" strategy is if you are the disruptive upstart: you have small market share, so your losses (tangible and intangible) will be lower compared the losses suffered by the fat lazy high-multiples incumbent who must satisfy angry shareholders when they see profit eroding.
I could be wrong, but "network effects" is a recent phenomenon and business schools haven't really taught students about it much. Either way, we have very little history for assets that appreciate in value the more they are used. Traditionally it's been the exact opposite. In fact, this concept basically doesn't exist in finance other than translations into FCF...but depreciation does.
Although things like Uber may be a different beast. They basically got big enough that cities were willing to push aside all of these special interest rules that kept the taxi industry crappy. So by dumping their product and acquiring customers, they were able to change the legal environment and infrastructure around them.
But they are also at a huge disadvantage because they changed it for everyone behind them as well. Lyft doesn't have to burn money as fast and gets all the same benefits for scale. Under their current market position, the minute Uber starts raising prices, they die.