  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.
