Equilibrium in local marijuana games

Abstract

We examine black market marijuana agriculture with the tools of game theory, population biology, and marginal analysis. A local marijuana game (LMG) is a nonlinear dynamical system, the totality of optimizing behavior of Growers, Ripoffs, and Narcs in an environment where agent behavior does not affect the constant marijuana price. Growers grow, Ripoffs steal, and Narcs eradicate and arrest. Growers resemble K-strategists, Ripoffs resemble r-strategists, and Narcs resemble predators. We study two types of LMG equilibria: n-person game-theoretic equilibria and ecological steady-state carrying capacities. The population ratio of Growers to Ripoffs drives the game-theoretic equilibria. We show that Narc increase induces Ripoff increase and that optimal Grower planting strategies resemble the optimal nesting strategies of many species. A minimal mathematical model describes the LMG carrying capacity as the maximal sustainable proportion of planted marijuana patchland given any agent mix. The carrying capacity defines a unique fixed-point equilibrium of the LMG dynamical system, and the LMG system quickly converges to it exponentially. A simple testable relationship describes this equilibrium patch proportion P_e: P_e = 1 — (r + n)/g. The equilibrium analysis applies with change of coefficients to black market poppy and coca shrub agriculture. We discuss extensions to similar games, including the “border game” played by Aliens, Bandits, and Patrols.