Abstract
Game theory suggests that, in oligopolistic markets characterized by nonprice competition, dominant incumbents can use product proliferation to occupy a region of the product space (i.e., a subspace) and deter rivals from imitating their products. In part, this is because product proliferation makes the introduction of close substitutes comparatively less profitable; in part, it is because the strategy conveys a threat of retaliation to potential imitators. Yet this threat is only credible if the proliferator has high costs of exit from the occupied region of space. We hypothesize that complexity, as a property of product (sub)spaces, generates exit costs for the proliferator and increases the deterrent power of its strategy. We test this hypothesis by studying sequential product introductions in the U.S. recording industry, 2004–2014.