Infection-Curing Games over Polya Contagion Networks

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.