# A game theoretic treatment of contagion in trade networks

## TL;DR

This paper introduces a game theory model to study how infection risks in trade networks, like wildlife or lumber trade, are influenced by economic decisions and network structure.

## Contribution

A novel game-theoretic model that captures bidirectional feedback between trade decisions and contagion risks in networks.

## Key findings

- The probability of infection converges to a fixed point in acyclic trade networks with stochastic infections.
- The model identifies equilibria by computing best responses based on network structure and infection risks.
- It provides insights into global and individual risk drivers in trade networks with contagion.

## Abstract

Global trade of material goods involves the potential to create pathways for the spread of infectious pathogens. One trade sector in which this synergy is clearly critical is that of wildlife trade networks. This highly complex system involves important and understudied bidirectional coupling between the economic decision making of the stakeholders and the contagion dynamics on the emergent trade network. While each of these components are independently well studied, there is a meaningful gap in understanding the feedback dynamics that can arise between them. In the present study, we describe a general game theoretic model for trade networks of goods susceptible to contagion. The primary result relies on the acyclic nature of the trade network and shows that, through the course of trading with stochastic infections, the probability of infection converges to a directly computable fixed point. This allows us to compute best responses and thus identify equilibria in the game. We present ways to use this model to describe and evaluate trade networks in terms of global and individual risk of infection under a wide variety of structural or individual modifications to the trade network. In capturing the bidirectional coupling of the system, we provide critical insight into the global and individual drivers and consequences for risks of infection inherent in and arising from the global wildlife trade, and any economic trade network with associated contagion risks.

When networks of stakeholders trade goods that can become contaminated with an infection, like animal diseases in the pet trade or wood pests in the lumber trade, there is a trade off between minimizing cost and maximizing health and safety. The most efficient choice for each stakeholder is determined by the entire trade network of which they are a part. This paper introduces a model that can be used to understand the relationship between the structured of the network and the individual outcomes influenced by economic and ecological feedback loops throughout the trade network.