what are the types of market models?

Answer 1

Is this a micro or macro question? Then I can help a little more.

Answer 2

I believe you are talking about perfect competition and imperfect competition.

Perfect competition is were there is no predominant player in the market and all producers are price takers.

Then there is imperfect competition which is usually represented by oligopolies and monopolies.
Oligopolies are market systems were there are a few dominant players which can influence the market and a monopoly is a system that has one player that dominates the market.