Most prior research on the tendency for groups to be less cooperative than individuals (the interindividual-intergroup discontinuity effect) has used the Prisoner's Dilemma Game (PDG). Experiment 1 examined the discontinuity effect with 3 additional matrices: Chicken, Leader, and Battle of the Sexes (BOS). Unlike the PDG, these matrices are characterized by correspondence of outcomes. The discontinuity effect was significant for the PDG and Chicken matrices only. With the BOS and Leader matrices, both individuals and groups pursued outcome maximization through coordinated turn taking. Despite the lesser competitiveness, sets of interacting participants in the BOS and Leader conditions did perceive that they were 2 groups. Experiment 2 examined the discontinuity effect in 2 Chicken matrices with varying outcomes associated with mutual competition. Consistent with the doctrine of mutual assured destruction, the discontinuity effect was eliminated for the matrix in which mutual competition was associated with very low outcomes. Although concern for relative in-group standing gave rise to intergroup competition even in the domain of correspondent outcomes, such concern was constrained to the extent that it interfered with outcome maximization.