We study interfirm price competition in the presence of horizontal and vertical intrafirm conflicts in each firm. Intrafirm conflicts are captured by a principal-agent framework with firms employing more than one agent and implementing a tournament incentive scheme. The principals offer premium incentives in the sense of revenue shares to which agents react by proposing a sales price. Introducing such intrafirm conflicts results in higher prices and lower effort levels. Increasing the number of agents lowers the optimal surplus share of the agents as well as the individual effort and the sales prices. Firm profits first increase and then decrease when employing more and more agents suggesting that principals should employ an intermediate number of agents.