Economic Competition and the Structure of the Competition Graph of Random Networks

Abstract As the competition graphs of trade networks begin to garner attention from economists, a better understanding of their expected structure is important for studying real-world trade networks and their competition graphs. This paper has two purposes. First, it serves to encourage the adoption of competition graphs as a tool for studying competition in economic networks. Second, it studies the structure and dynamics of competition graphs derived from random directed networks of the form $$\mathcal {D}(n,p)$$ . The results presented here characterize the probabilities that certain foundational structures exist in the competition graph of a random graph, and describe the density and connectivity of the competition graph of a random graph. Structural dynamics of these competition graphs are also studied. In particular, the results show that competition graphs are typically more dense than the networks they are derived from. Finally, these results are used to generate a discussion motivating the use of competition graphs in the economics literature.