The market for ride sharing is starting to look like a pie-eating contest where the prize is . . . more pie.

Lyft went public March 29, and the stock almost immediately went into a steep decline as investors belatedly noticed that the company hadn’t made any money yet and didn’t have any clear plans to do so.

On April 11, Uber filed the prospectus for its own initial public offering. The company said it commands more than 50 percent of the ride-hailing market in the Americas and Europe — and had an operating loss of $3 billion last year, about three times as much as Lyft lost.

Think about that: Collectively, those two companies lost nearly $4 billion in a single year ferrying people — and other stuff — hither and yon.

Both companies have a wildly successful product and a loyal customer base. The companies are also locked in a price war. And thus, they have together blown through tens of billions of dollars of venture capital. Having presumably exhausted that source of funds, they are offering retirement funds and institutional investors the opportunity to pour their money down the same hole.

Those investors would presumably like to get their money back at some point, which means that this incineration of capital must eventually stop. But for the moment, neither company seems willing to call a price-war cease-fire. For investors to recover their money, and for ride hailing to survive, one of these companies may need to die.

What’s happening in the ride- sharing market is typical of industries with massive overcapacity. In those markets, whether airlines or steel, too much capacity means brutal price wars until some of the combatants are annihilated, and the victors gain enough pricing power to cover their production costs. To be sure, you don’t usually see this pattern in markets that are already dominated by only two competitors, as is the case for ride hailing in the United States. But ride sharing is special in a number of ways.

First, it offers what economists call “network effects”: The more riders you have, the easier it is to attract and dispatch drivers, and the more drivers you have, the more riders you will attract. Markets that display network effects tend to consolidate toward a handful of players, and possibly only one.

Second, ride sharing has low switching costs. It’s simple to install both apps on your phones, and many riders and drivers do just that, the better to comparison shop. Which means fierce competition over every single ride.

Third, Uber and Lyft aren’t in competition with only each other; they’re competing with conventional taxis. And public transportation. And your personal automobile, not to mention your bicycle, moped or feet. Eventually, if the companies can make people dependent enough on ride hailing , they might be able to raise prices a bit and still retain most of their customer base. But “eventually” keeps receding over the horizon — and in the meantime, they’ve also got to undercut each other.

There are only two ways that the price war can end. Either Uber and Lyft come to some sort of tacit agreement to stop selling their services below cost, or at least one of the companies goes bankrupt.

Halting the price wars may well be easier to do when both companies are public, and communiques about their pricing strategies can be explained as legally required SEC filings, with no whiff of collusion. But that doesn’t mean they necessarily will reach an armistice. Uber has historically been a bare-knuckle brawler rather than a diplomat, and it may well decide to keep burning cash on the assumption that the company can raise a bigger war chest than Lyft.

And even if they do stop sniping at each other, the bloodshed won’t necessarily cease. The assumption that there’s some profitable equilibrium, either a monopoly or a cartel, rests on the assumption that the capacity glut is caused by the presence of other ride-hailing firms.

But there are a lot of cars in the world and a lot of people with driver’s licenses. There’s always a risk that some of those drivers will jump into the market and start competing with Uber and Lyft.

The dispatch services that Uber and Lyft provide are undoubtedly valuable and harder for competitors to copy than “a guy in a car.” But are they valuable enough to keep riders from using smaller upstarts? Maybe not, if those upstarts charge a little less for the ride.

And so the pie-eating contest may continue forever, until everyone bursts. There may ultimately be no route to profitability for these firms, no payoff for investors. The sustainable number of major ride-sharing companies may not be two, or even one, but none.

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