How do value creation and competition determine whether a firm appropriates value?

How does competition among economic actors determine the value that each is able to appropriate? We provide a formal, general framework within which this question can be posed and answered, and then provide several results. Chief among them is a condition that is both required for, and guarantees, value appropriation. We apply our methodology to (i) assess the familiar notion that uniqueness, inimitability, and competition imply value appropriation, and (ii) determine the value appropriation possibilities for an innovator whose unique discovery is of use to several others who can compete for the right to use it.