Exchange, raiding, and the shadow of the future

Abstract

A two-period exchange model is developed where production decisions in the first period determine the amount of resources available in the second period. Each agent allocates resources to defend its production and attack the production of the other agent. Production, conflict and exchange occur simultaneously in a dynamic model. This extends earlier exchange models, which are static and preclude defense and appropriation. The agents jointly determine price through their export decisions. Upon introducing exchange endogenously, raiding in the first relative to the second period decreases with growth, appropriation cost, and when the future becomes more important, and increases with defense cost, production cost, and usability of appropriation. Increasing the usability of appropriation and defense cost causes a transition from pure exchange via joint exchange and raiding to pure raiding. This implies that agents gradually substitute from defense to appropriation, they exchange less, and utility decreases. Utility isoquants in a usability of appropriation versus discount factor diagram are concavely increasing for joint exchange and raiding, and can be convexly decreasing for pure raiding. Cobb–Douglas utilities are assumed. The results are confirmed with CES utilities.