Members of an illegal armed organization reveal their desertion minimum values in reaction to the incentives offered by a government. Depending on the organization's network structure, the desertion of an individual member will unleash a contagion process that will destroy the local network at a varying speed. Staging a game between a government and the members of an illegal organization, connected through a network structure, we show that the speed of the desertion process depends on the network structure and on its members' minimum desertion values.