[yumario]

Yes it oversimplified. Suppose that a = b, i.e both companies has the same market share. Also suppose that when both companies has equal market share their innovations rates are the same, same price etc. The model has two equilibrium both companies compete in which their market share fluctuates around a = b. and we get a sort of predator-pray model[1]. Both companies do not compete their market share stays the same.

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...

[RussianCow]

The issue with this is the scenario where either company deviates from the status quo. For example, company A decides to make a tradeoff: invest more into R&D at the expense of sales and marketing. If Company B remains the same, company A may suffer a temporary dip in sales, but in exchange, their product becomes better over time and they are able to take more than the original 50% of the market due to having a superior product.

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

[yumario]

I think a clearer is example would be with telecom companies. Say A and B, are telecom with equal market share. A, could "compete" in an attempt to gain market share and install a gigabit bandwidth, but this will only cause cause company B to retaliate and instant gigabit bandwidth as well. Therefore the market share and revenue will fluctuate back to equal. But both companies would have lose the money involved in installing the higher bandwidth. Therefore if the market share is equal the best strategy would be "tic for tac" i.e wait until you opponent does something. Which has two equilibrium either constant tic for tact. Or waiting for the opponent does a move.

In the case when one company's market share is smaller than the other it is always better to "invest" or compete.

[RussianCow]

There is always an advantage to being first; if there wasn't, nobody would ever invest in anything new. Even in your example, the first company to bring gigabit internet to an area can secure some contracts that will still be in place when their competitors respond, so they get a head start when that does happen, which can lead to a longer term market share advantage if they can keep the momentum going. Even if that advantage doesn't last forever, it certainly makes them a lot of money in the meantime.

See: Uber vs Lyft, the iPhone (and, historically, many other Apple products), Coca-Cola, Netflix, etc.

[yumario]

I don't think that's the heart of the question. My question is is better for innovation if two companies have equal market share or if one has a smaller market share? I trying to argue that it is better if one company has a smaller market share.

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.

[RussianCow]

> My question is is better for innovation if two companies have equal market share or if one has a smaller market share?

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.

[yumario]

Yeah, when threadripper came out I believe it offered the same performance as intel I9 for about half the price. Why did AMD choose such aggressive pricing? Because they have the desire to grow. If Intel and AMD had the same market it would not make sense to put out a product for half the price as your competitor. So if Intel and AMD had the same share, we would probably still paying 1000+ dollars for intels I9.