From Longman Business Dictionary
competecom·pete /kəmˈpiːt/ verb [intransitiveI]COMMERCE when one company or country competes with another, it tries to get people to buy its goods or services rather than those available from another company or countrymeasures to enable Irish industries to compete effectively in Europe
compete withIt has to keep its own prices down so that it can compete with other major electricity suppliers.
compete forIf the pound continues at this level our exporters can’t compete for sales across the Atlantic.