A contestable market is one:

without barriers to entry. with duopoly. with external effects. that eliminates consumers' surplus.

Why has game theory been used to explore the workings of oligopoly?

Game theory is useful in capturing the complications caused by the difficulties of entry and exit. Game theory is useful in exploring power of any kind, including the market power of dominant sellers. Game theory is useful in exploring interdependence, which is a key feature of oligopoly. Game theory is useful when dealing with firms that do not want to maximize profits, as is often the case in oligopoly.