I am not sure that such a thing can exist. For a market to exist it must function. If it doesn’t function it’s not a market but the lack of one. So it’s not logical.  As Bertil Hatt asks, you can mean a market that exhibits certain categories of failure, or a market that is inefficient. But not a non-functioning market.  Can you clarify wat you’re asking?  GIve us some context? https://www.quora.com/What-is-a-non-functioning-market