This paper investigates the existence of market power and the sequentiality of games in the crude oil market. In particular, we examine whether Saudi Arabia acts as a Stackelberg leader or in a simultaneous-move framework, in a number of market power scenarios ranging from perfect competition to cartel. We develop a numerical simulation model that is formulated as a complementarity problem, allowing for the possibility of strategic interaction between the players. In contrast to other partial equilibrium models of natural resource markets, the model proposed in this paper explicitly takes into account the influence of price pools such as Brent and WTI where arbitrageurs exploit price differentials that are not justified by transport costs. Our results indicate that all suppliers exert market power while Saudi Arabia acts as Stackelberg leader. More specifically, we find that OPEC members do not act cooperatively, i.e. they do not maximise joint profits. Rather, they exhibit strategic non-cooperative behaviour, rejecting the notion that OPEC is a cartel