Analysis of Heuristic Techniques for Controlling Contagion

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, recent research has used novel heuristic oracles in a double oracle formulation to generate mixed strategies. However, these heuristic oracles were evaluated only on runtime and quality scaling with the graph size. Given the complexity of the problem, numerous other problem features and metrics must be considered to better inform practical application of such techniques. Thus, this work provides a thorough experimental analysis including variations of the contagion probability average and standard deviation. We extend the previous analysis to also examine the size of the action set constructed in the algorithms and the final mixed strategies themselves. Our results indicate that game instances featuring smaller graphs and low contagion probabilities converge slowly while games with larger graphs and medium contagion probabilities converge most quickly.