Task colocation improves datacenter utilization but introduces resource contention for shared hardware. In this setting, a particular challenge is balancing performance and fairness. We present Cooper, a game-theoretic framework for task colocation that provides fairness while preserving performance. Cooper predicts users' colocation preferences and finds stable matches between them. Its colocations satisfy preferences and encourage strategic users to participate inshared systems. Given Cooper's colocations, users' performance penalties are strongly correlated to their contributions to contention, which is fair according to cooperative game theory. Moreover, its colocations perform within 5% of prior heuristics.