This thesis considers a model of Coumot competition where firms have incomplete information about their rivals' costs. The equilibrium concept we use is that of Bayesian- Nash equilibrium. Based on the recognition of the "aggregative structure" within Coumot competition in which each finn's payoff is determined by her own strategy choice and the unweighted sum of all firms' strategy choices, we are able to characterise equilibria in a very simple way. We show that when we consider not the best response but the strategy consistent with a Nash equilibrium in which the aggregate strategy of all players take same value (which is given by what we call the replacement function), then Nash equilibria correspond to fixed points of the aggregate replacement function whose properties we can certainly obtain without need for restricting our attention to symmetric games or games in which there are just 2 players. We develop sufficient conditions under which there is a unique equilibrium. The approach facilitates the analyses of competitive limit and comparative statics, since the characterisation of Bayesian-Nash equilibria can be shown on a two-dimensional space. We also examine two applications, which include information sharing and the relative efficiency of an ad valorem tax scheme as opposed to a specific tax scheme.