Criminal networks and the authorities: an integrated equilibrium framework for disrupting illicit product trade

We develop an integrated equilibrium framework for the disruption of illicit product trade. A criminal network and the authorities compete in a noncooperative game that leads to a Nash Equilibrium, rather than in the more common Stackelberg structure in which one player leads and the other follows. The criminal network selects illicit product shipments over multiple supply markets, multiple demand markets, and multiple transportation routes that join them. What emerges is a spatial price equilibrium in which the supply and demand prices are determined within the model and clear the markets. The authorities allocate a finite budget across the routes in order to disrupt the trade. They evaluate that allocation through a multicriteria objective, one that weighs the disruption achieved against the monetised societal benefit of enforcement, with a weight that governs the balance between the two. We formulate the equilibrium conditions as a variational inequality problem and then derive alternative formulations of it. We establish monotonicity, along with conditions under which a modified projection method converges, and that method yields closed form expressions for the product shipments, the budget allocations, and the Lagrange multiplier at each iteration. The framework applies to illicit trade in drugs, minerals, counterfeit personal protective equipment, cybercrime in financial services, and stolen grain. We then present a realistic case study on stolen grain from the occupied territories of Ukraine, calibrated entirely from open sources. In the computed equilibria, enforcement erodes criminal revenue and raises the prices that consumers pay, the societal benefit weight shapes the budget allocation, and disrupting transportation corridors suppresses the trade while pressure on a single destination market only displaces it.