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The use of game theory to model conflict has been studied by several researchers, spearheaded by Schelling. Most of these efforts assume a single payoff matrix that captures players' utilities under different assumptions about what the players will do. Our experience in counterterrorism applications is that experts disagree on these payoffs. We leverage Shapley's notion of vector equilibria, which formulates games where there are multiple payoff matrices, but note that they are very hard to compute in practice. To effectively enumerate large numbers of equilibria with payoffs provided by multiple experts, we propose a novel combination of vector payoffs and well-supported ε-approximate equilibria. We develop bounds related to computation of these equilibria for some special cases and give a quasipolynomial time approximation scheme (QPTAS) for the general case when the number of players is small (which is true in many real-world applications). Leveraging this QPTAS, we give efficient algorithms to find such equilibria and experimental results showing that they work well on simulated data. We then built a policy recommendation engine based on vector equilibria, called PREVE. We use PREVE to model the terrorist group Lashkar-e-Taiba (LeT), responsible for the 2008 Mumbai attacks, as a five-player game. Specifically, we apply it to three payoff matrices provided by experts in India--Pakistan relations, analyze the equilibria generated by PREVE, and suggest counterterrorism policies that may reduce attacks by LeT. We briefly discuss these results and identify their strengths and weaknesses from a policy point of view. [ABSTRACT FROM AUTHOR]