In economics, the word competition means that there are at least two competitors (¨players¨) who want to get a share of a market. The market is divided between all the economic players; this means that if a player gets a higher market share, another player will get a smaller share of the market. In his work, The Wealth of Nations, Adam Smith says that all players uses the resources they have so that they will get the most profit from these resources. According to Smith, this encourages efficiency. Game theory looks at competition, from a mathematical point of view.
Note that competition does not necessarily involve different companies; in the 1920s, General Motors had divisions that overlapped, and that competed for resources. Procter & Gamble introduced the competition between different brands in the 1930s.
Also note that competition is limited: In some areas, there are monopolies, often granted by the state. The state may also apply taxes or pay subsidies as a way to protect its own economy.
Other factors that limit competition include the existence of cartels.