Perhaps you haven't gotten the memo. AA is making money - lots of it. Indeed, this year they're projected - by some estimates - to make more of it than any other airline in the U.S., including precious Delta. They just may not be making much of it, on a standalone segment basis, on all their routes to Asia. Nonetheless, they obviously feel that is a worthwhile investment in operations that may lose money on a standalone basis but contribute an overall positive halo effect to both the top and bottom lines. You know, sort of like all the money that Delta has lost for years in NYC, and on their little oil refinery expedition - loss making in isolation, but overall worth the investment.
But back to the actual topic - AA's growth in Asia, particularly from LAX, and the reality that Delta fighting AA for (supposedly) money-losing market share LAX-Asia would be a disastrous waste of Delta shareholder capital, which is precisely why I suspect that it won't happen, and if it does, it won't last long.
There is strategic logic to AA investing in losses in order to build a gateway at LAX. AA, as we are ever-so-constantly reminded, lacks a west coast gateway to compete with SFO or SEA, but does have a very strong local presence in LAX, including a very strong if not dominant position among corporate traffic in key sectors, dense coverage of major O&D markets, and alliances with some of the airport's largest foreign operators. Again - logic.
Now let's look at Delta. Is there any major legal, regulatory or operational roadblock stopping Delta from adding another five flights per day from LAX to Asia? No, not really. Delta is running out of gate space because it's hemmed in by competitors, but could probably manage that. The larger question though, is why? Why on earth would Delta do such a thing? There is absolutely no strategic logic to it - Delta would be wasting, not investing, money on something that would be virtually guaranteed not to pay off. Unlike for AA, LAX serves no network role for Delta that isn't already handled by SEA.
So here's where the multi-step thinking comes in. Say AA adds flights to ICN, PEK, HKG and AKL, and Delta adds a flight to each right on top of AA. Then what? If the markets were going to lose money for AA, then they sure will for AA and Delta once even more capacity is dumped into them. And to what end? That type of behavior would typically be designed to force AA to retreat from these markets, but for the reasons already mentioned, I doubt that would happen here. Again, AA is in a better position at LAX (larger local presence, more gates, etc.) than Delta, is in pretty much as good or better a position than Delta in most of those foreign markets, and - perhaps most importantly - AA has more cash to burn and needs LAX more.
Following through on this little game theory, Delta would destroy shareholder value to punish a cash-rich competitor, and at the end of it I think a good case could be made that Delta would have accomplished nothing in terms of forcing AA out of those markets, and burned through cash in the process. I would absolutely love to hear Richard Anderson - who is typically a fairly reasonable, sensible guy (recent horribly chosen words about the ME3 notwithstanding) - explain this brilliant plan to shareholders. But I don't think I'd get the chance. Because again - it makes absolutely no sense whatsoever, and if it ever did happen, I suspect it would quickly end.