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I study the economic implications of the world oil market dominated by OPEC and non-OPEC major oil producing countries using a general equilibrium model of trilateral trade with oil duopoly. There are three countries and three goods, x, y, and oil (z). Home (H) is endowed with good x . Foreign (F) is endowed with good y and also produces oil (z). Middle (M) is an oil producing country and supplies oil only. I consider two types of oil market structure; (1) Cournot duopoly and (2) perfect competition. I find that Foreign is actually worse off under Cournot duopoly despite being a duopolist for wide range of parameter values that reflect real world situations. This is mainly due to reduced consumption of oil and reduced value of good y endowment under duopoly when Foreign is a net oil exporter or oil autarky, and is also due to worsening terms-of-trade effect under duopoly when Foreign is a net oil importer. Welfare reversal with higher welfare of Foreign under oil duopoly occurs only under highly unrealistic parameter values, and hence the main results of the study remain robust.