From the game theorist point of view I think its better if one company is the underdog. Think about it, if one company is the underdog, one company has a lot to gain by competing, while the other has a lot to lose if they don't compete. Therefore we get competition.
Now, the more equal the market share of the companies the grater the risk and less the reward for competition... A better strategy would be not to undercut your competitor and instead divide the market share. Which leads to stagnation.
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.
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.