Competition is one of the most important concepts in economics, yet when examined closely, it turns out to be one of the most elusive concepts to nail down in practice. A market in some particular good or service is said by economists to be "competitive" if a substantial number of buyers and sellers trade in the good or service independently and thus no single buyer or seller is so "weighty" in the marketplace as to significantly influence the going price of the good or service by his/her individual decisions about how many units he personally will buy or sell.
The practical problems (and disagreements) in assessing whether a particular market is "competitive" or not arise when you look at the real world and try to specify the geographic boundaries of the market and the breadth or narrowness of the definition of the good on which you are focussing. Billy-Bob Motors may have the only Ford dealership in town, giving him a "monopoly" in some very narrow sense -- but local car buyers will be quick to travel to other Ford dealerships in any of a number of other cities or towns if Billy-Bob tries to take advantage of his monopoly by jacking up the price and then word gets around (perhaps through advertising) that there are noticeable advantages in the deals offered on Fords elsewhere. The bigger the price differential and the lower the transportation costs between seemingly distinct market areas, the larger the effective market area really becomes. Similarly, dealerships in Chevrolets, Plymouths, Volkswagens, Toyotas, Nissans, Volvos, Fiats, Hyundais, and Hondas are not selling exactly the same products as Ford dealerships (even Fords come in various models), but they sell very close substitutes for Fords that many buyers will turn to if the price of a new Ford at Billy-Bob's seems out of line. Used car dealers, estate sale auctions, bankruptcy liquidators and ordinary citizens selling their old cars through newspaper ads provide still other sources of supply for slightly less close substitutes for a brand new Ford. Even taxis, bus systems, rent-a-car agencies, subway systems, railroads, tractors, motorcycles, motorscooters, mopeds, bicycles, roller skates, dog-sleds and "shanks' mare" constitute partial substitutes for Ford ownership as a method of getting around from point A to point B and thus have a "competitive" restraining effect on pricing in the local market for Fords (which may be seen as only a part of some much broader market in means of personal transportation).
The bottom line -- competitiveness in markets is a matter of degree, and the observer's assessment of the degree of competitiveness in concrete instances will be heavily influenced by the observer's initial assumptions about the geographic extent of the market area and the breadth or narrowness of his definition of the good or class of goods that constitute equivalent products.