Background/Question/Methods Mutualistic species vary in their level of partner specificity, which has important evolutionary, ecological, and management implications. Yet, the evolutionary mechanisms which underpin partner specificity are not yet fully understood. Most work on specialization focuses on the trade-off between generalism and specialism, where specialists receive more benefits from preferred partners at the expense of benefits from non-preferred partner, while generalists receive similar benefits from all partners. Here, we highlight an additional dimension of specialism in mutualists, based on the fact that all mutualisms involve some degree of cooperation but also some degree of conflict between the partners. Specialization to a particular mutualistic partner can be either cooperative, increasing benefit to both the focal species and the partner, or antagonistic, maximizing resource extraction from the partner at that partner's expense. We devise an evolutionary game theoretic model to assess the ecological and evolutionary dynamics of cooperative specialization, antagonistic specialization, and generalism. The model features a host species that contains a generalist and two specialist phenotypes that specialize on one of two partner strains or species. Results/Conclusions Our model shows that cooperative specialization can lead to bistability: stable equilibria with a specialist host and its preferred symbiont excluding all others. We also show that generalists can persist in two ways under cooperative specialization with spatial effects: 1) Generalists can thrive at the boundaries between differing specialist patches if generalist benefit exceeds average specialist benefit, or 2) Specialists may evolve toward generalization if the tradeoff between matching with a preferred symbiont and mismatching with a non-preferred symbiont is concave down. Under antagonistic specialization, if average specialist payoff exceeds generalist payoff generalists become extinct and the frequency of specialists cycle, otherwise, the generalists exclude the specialists. We provide predictions for how a cooperation-antagonism continuum may shape the patterns of partner specificity that develop within mutualistic relationships. In our model it is possible for both generalist and specialist host phenotypes to coexist when specialization is either antagonistic or cooperative, though the population dynamics associated with both modes of specialization are distinct.