In this dissertation, I combine theoretical and empirical approaches, as well as concepts from the human and non-human animal literature, to investigate the effect of different types of competition on cooperation among members of a social group. These lines of research are complementary and mutually reinforcing: drawing on approaches developed to analyze the behavior of one taxon to investigate another can help us elucidate universal principles governing the evolution of cooperation and conflict over resource division. In chapters 1 and 2, I apply game theoretic "tug-of-war" models of reproductive skew to conflict over resource contribution and division within human groups. In chapter 1, I consider competition over individuals' personal resources. The results of a laboratory economic game support the theoretical prediction that the potential for such competition favors cooperative contribution to an equally shared group resource from which everyone benefits. In chapter 2, I relax the assumption of equal sharing, and demonstrate theoretically and empirically that competition over resource division leads to lower contributions and payoffs. In chapters 3 and 4, I extend a tug-of-war model of intergroup competition to investigate conflict over resources shared among social insect colonies. I focus on the primitively eusocial wasp Polistes dominulus, as individuals display behavioral flexibility and benefit from investing in both cooperation and conflict. In chapter 3, I use field and lab experiments test theoretical predictions that P. dominulus may not face a simple tradeoff between within-group cooperation and competition. In chapter 4, I demonstrate mathematically that asymmetries among group members in relatedness and dominance affect cooperation and conflict within insect societies engaged in intergroup competition. In chapter 5, I consider competition over foraging contributions in P. dominulus, and show in a field manipulation that aggression towards experimentally removed workers is higher when these wasps received food while they were in the lab. This leads to questions about the possible function of aggression in within-group competition and cooperation in this species.