Cooperation in Networks: Mathematics of Metrics and Utility

Introduction: The Army’s social networks often involve cooperation – entities working together to achieve a common goal. What are the metrics for such a network? What is cooperation and what makes cooperative networks effective? Can network structures and processes enhance cooperation and optimize networks? This presentation uses the emerging mathematical framework of subset team games (Arney & Peterson 2008), which provides a theory of the principles, relationships, and metrics of cooperative phenomena. The subset team game framework is focused on agents (network entities) working together for a common good, reflecting the team-oriented cooperation that characterizes social and military networks. The underlying assumption of subset team games is that players are motivated by a combination of selfish and altruistic reasons, and the framework provides computable metrics from the network’s utility. The framework provides derived metrics of an agent’s selfish contribution, altruistic contribution, and total contribution from a carefully defined utility function.