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Coevolution is one of the major drivers of complex dynamics in population ecology. Historically, antagonistic coevolution in victim‐exploiter systems has been a topic of special interest, and involves traits with various genetic architectures (e.g., the number of genes involved) and effects on interactions. For example, exploiters may need to have traits that "match" those of victims for successful exploitation (i.e., a matching interaction), or traits that exceed those of victims (i.e., a difference interaction). Different models exist which are appropriate for different types of traits, including Mendelian (discrete) and quantitative (continuous) traits. For models with multiple Mendelian traits, recent studies have shown that antagonistic coevolutionary patterns that appear as matching interactions can arise due to multiple difference interactions with costs of having large trait values. Here we generalize their findings to quantitative traits and show, analogously, that the multidimensional difference interactions with costs sometimes behave qualitatively the same as matching interactions. While previous studies in quantitative genetics have used the dichotomy between matching and difference frameworks to explore coevolutionary dynamics, we suggest that exploring multidimensional trait space is important to examine the generality of results obtained from one‐dimensional traits. [ABSTRACT FROM AUTHOR]