Allocating ideas: Horizontal competition in tournaments

We develop a stylized model of horizontal and vertical competition intournaments with two competing firms. The sponsor cares about the qualityof the design but also about the design location. A priori not even thesponsor knows his preferred design location, which is only discoveredonce he has seen the actual proposals. We show that the more efficientfirm is more likely to be conservative when choosing the design location.Also, to get some differentiation in design locations, the cost differencebetween contestants can neither be too small nor too big. Therefore, ifthe sponsor mainly cares about the design location, participation in thetournaments by the two lowest cost contestants cannot be optimal for thesponsor.