# Infection-Curing Games over Polya Contagion Networks

## TL;DR

This paper models infection control as a game over a network using Polya urns, establishing the existence of Nash equilibria for infection levels and providing computational methods and simulations to analyze strategic interactions.

## Contribution

It introduces a novel infection-curing game model based on Polya contagion networks and proves the existence of Nash equilibria using proxy measures and numerical algorithms.

## Key findings

- Nash equilibrium exists for the infection game.
- Gradient descent algorithms can compute equilibrium strategies.
- Simulations support theoretical results on small networks.

## Abstract

We investigate infection-curing games on a network epidemics model based on the classical Polya urn scheme that accounts for spatial contagion among neighbouring nodes. We first consider the zero-sum game between competing agents using the cost measure for the average infection in the network. Due to the complexity of this problem we define a game on a proxy measure given by the so-called expected network exposure, and prove the existence of a Nash equilibrium that can be determined numerically using gradient descent algorithms. Finally, a number of simulations are performed on small test networks to provide empirical evidence that a Nash equilibrium exists for games defined on the average network infection.