AMD has always been nipping at Intel's heels, for 20+ years now, never really losing or gaining too much to pose a real threat. Yet we've seen how ruthlessly Intel will snuff out potential contenders (such as Transmeta, RIP), it does kind of make you think there's something to it.
Sold those shares way too early in hindsight, but still got a good return out of that thinking, and if AMD ever gets into trouble again, I won't hesitate to apply the same logic.
Do Nvidia integrated gpu (mpgu) exist?
Nnvidia claims they exist but all their weblinks to details are dead. https://www.nvidia.com/object/main_mobo_gpus.html
It is nearly impossible to maintain an oligopoly in a market that is easy to enter and questions of underdog/overdog become irrelevant. All companies have to offer a reasonable (value/$) proposition to customers of they go broke.
[0] Poor Nokia - http://www.asymco.com/wp-content/uploads/2012/02/Screen-Shot...
The patents on the core of x86_64 will expire in a couple years. Even if you can't have the more recent vector instructions, that's pretty good for a lot of use cases.
A's reward for competing will be n - a = b.
A's risk for competing will be a, (it's remaining market share).
A's will compete as long as the reward is greater than risk.
This will reach an equilibrium at a = b.
I would say that your a and b could be like, levels of investment into researching. They'll research at some level, or risk falling too far behind, but can't spend too much as then they'll have to divert funds from other things like marketing or production, or just run out of money. They'll both likely choose to invest at a pace where they think they'll be able to match the other's innovation, but not so much as to overspend.
What does it means to compete? It could mean many things like not putting lower prices, delaying innovations until competitor has release their own etc.
[1] http://ccnmtl.columbia.edu/projects/seeu/dr/restrict/modules...
What you're talking about really only works if both companies agree to stay stagnant and collude to keep the status quo as-is. To be fair to your point, this has happened a few times historically, but it is usually considered price fixing and is very illegal[0].
[0]: https://en.wikipedia.org/wiki/Price_fixing#United_States
In the case when one company's market share is smaller than the other it is always better to "invest" or compete.
See: Uber vs Lyft, the iPhone (and, historically, many other Apple products), Coca-Cola, Netflix, etc.
Case 1: Netflix. Netflix caused innovation in the movie rental industry. But when Netflix first began it had much smaller market share compared to blockbuster. Would Netflix innovate again? Sure, but I doubt it would do anything revolutionary again. Most likely it would grow stagnant, once the new market stabilizes between hulu, HBO, disney, amazon etc.
Case 2: Apple. Apple was the underdog in early 2000s and that caused then to innovate, while Microsoft had grown stagnant. Today both Apple and Microsoft sort of have similar market shared and they don't really compete with each anymore. Microsoft shifted to cloud, and dropped windows phone. Apple keeps doing what they are doing with marginal upgrades to iphones, and mac. I don't really expected to come up with another "iphone" level innovation any time soon.
Case 3: Amazon. No big company is really trying to compete with amazon this days. I don't see Google or Facebook coming up with own online stores. It just not worth it to compete. While they are a lot of smaller online stores.
Case 4: Automobile industry. Sure they are new car models each year...but it is nothing revolutionary. Simple marginal upgrades over last year model. It was not until an underdog (tesla) tried to gain market share that we have seen any sort of innovation from them.
Most of the innovation today happens at smaller companies, and they eventually either succeed and become the next Apple and Google, fail and go out of business, or they get bough by the big companies.
If that's your question, then the answer is obvious, isn't it? The higher the potential reward, the more motivation to innovate. If you only control 1% of the market, innovating might easily mean a 1000% growth of your company; but if you already own half, the best you can possibly do is double that. The upside just isn't there to justify big, risky plays.
That said, there is always a desire to grow, even if not by as much, so there is still incentive to not become stagnant and to continue making improvements to your products, even if marginal.
Do people here think it sound reasonable?
Edit: Mathematically the argument would be as follows:
Consider two company A and B. A has market share 'a' and B has b. n is the total market. Then a + b = n.
A's reward for competing will be n - a = b.
A's risk for competing will be a, (it's remaining market share).
A's will compete as long as the reward is greater than risk.
This will reach an equilibrium at a = b.