Global International Relations: An Algebraic Approach

• In Event: International Economics and War

Abstract

We develop a formal model of international trade and conflict. Our proposed angle of attack marries (smooth) systemic approaches with more traditional dyadic analyses. We study all the world’s states and all the world’s goods, as in the smooth systemic approach. In contrast with extant work in this vein, however, we study the states and the goods in the context of a given simplicial complex, which encodes both trade and war relations in a set-up flexible enough for monads, dyads, n-ads, or any k-adic intermediate. Though complicated, this simplicial complex ably characterizes the international system in a disaggregated way; we incorporate it into traditional analyses by allowing it to serve as a background parameter. Despite the necessarily-discrete algebraic structure of relations among (finite) states, we provide results on the existence and stability of international equilibrium. A series of vignettes highlights how the approach can work both on micro and macro scales, and we touch on extensions to resource extraction, globalization, and alliances.

Author

• Robert J. Carroll, University of Illinois at Urbana-Champaign