How Do Value Creation and Competition Determine Whether a Firm Appropriates Value?

We define value creation, competition, and value appropriation, and show that (i) there is a minimal level of value creation that is required if competition is to allow a firm to appropriate value; (ii) there is a higher level of value creation guaranteeing competition will result in value appropriation; (iii) there is a measure of scarcity, which we call minimum value, with the feature that competition implies a firm surely appropriates value if and only if the firm's minimum value is positive; and (iv) if an agent is to appropriate value, a particular structure of competition is required. Our results are relevant to the theoretical foundations of strategy. For example, we show that ownership of assets that are non-imitable and productivity-enhancing does not guarantee value appropriation