Many strategic actions carry a ‘contagious’ component beyond the
immediate locale of the effort itself. Viral marketing and peacekeeping operations have both been observed to have a spreading
effect. In this work, we use counterinsurgency as our illustrative
domain. Defined as the effort to block the spread of support for an
insurgency, such operations lack the manpower to defend the entire
population and must focus on the opinions of a subset of local leaders. As past researchers of security resource allocation have done,
we propose using game theory to develop such policies and model
the interconnected network of leaders as a graph.
Unlike this past work in security games, actions in these domains
possess a probabilistic, non-local impact. To address this new class
of security games, we combine recent research in influence blocking maximization with a double oracle approach and create novel
heuristic oracles to generate mixed strategies for a real-world leadership network from Afghanistan, synthetic leadership networks,
and scale-free graphs. We find that leadership networks that exhibit highly interconnected clusters can be solved equally well by
our heuristic methods, but our more sophisticated heuristics outperform simpler ones in less interconnected scale-free graphs.