How the competition behaves
In railroad tycoon 2, competing investors and companies are controlled by the game's artificial intellegence. As with most similar games, the artificial intellgence follows particular patterns which can easily be identified.
Competing companies will always start off by connecting two towns that are close together, each with at least 4 houses. They will use a relatively large number of trains for the short distance, mainly passengers and mail, but sometimes freight if there is an industry within the station's radius that is supplying something. The competition always builds double-track railway, and never builds electric track.
When there is enough cash on hand for the competing company, it will expand, it will connect a nearby town/city with a double track railway, and start running a few services to it. Whenever this happens you will get a notification. At every station it will build a small restaurant, a saloon and a post office. It will continue this expansion process, always connecting to nearby towns. Note that the competing company will never start an isolated rail system. The competition will never connect to a town already with a rail service.
Using this to your advantage
Since the competition will only connect to nearby towns, connect to nearby towns yourself, surround the competition with your own services. They will not expand. Also if you connect to every town on the map, you can sit back an relax because there won't be any more trouble from the competition.
Generally speaking when making connections the competitor will avoid using your own companies track. This is of course unless you own an essential piece of track, such as the only crossing point to get across a river. This might force the competition into using your piece of track, meaning you get a share of all their trains revenues.
About Investors
Be careful in the stock market, if you have bought a lot of shares on the margin and your purchasing power looks low, then you are vounerable to attack, other investors might suddenly sell off all their shares in that company, which causes the share price to collapse, putting your purchasing power below zero, and getting you caught in a margin call. Beware!