In a network confrontation, evader and detector look for optimal strategies on origin-to-destination trajectories and blocking arcs (with assigned detection probabilities) in a zero-sum matrix game with the mean capture probability as pay-off (Washburn & Wood, 1995). Related active research goes on, stimulated by multiple civil and military applications (Caulkins et al., 1993; Israeli, 1999; Bell, 2003). For multiple origins and destinations with pre-established quotas, the dimensional reduction of the evader problem (in the dual pair) to a standard maximum flow problem doesn't seem directly possible or analytically amenable. Herein an indirect approach, based on successive delimitations of the flow, is proposed, leading to an exact algorithm. Preliminary tests with limited-size problems and multiple simulations on a medium-size network of the literature have shown good computational performance.
quotas on networks; detection and evasion games; computational reduction
