Strategy dynamics are hypothesized to be a structural factor of interactive multi-actor design problems that influence collective performance and behaviors of design actors. Using a bi-level model of collective decision processes based on design optimization and strategy selection, we formulate a series of two-actor parameter design tasks that exhibit four strategy dynamics (harmony, coexistence, bistability, and defection) associated with low and high levels of structural fear and greed. In these tasks, design actor pairs work collectively to maximize their individual values while managing the trade-offs between aligning with or deviating from a mutually beneficial collective strategy. Results from a human subject design experiment indicate cognizant actors generally follow normative predictions for some strategy dynamics (harmony and coexistence) but not strictly for others (bistability and defection). Cumulative link model regression analysis shows that a greed factor contributing to strategy dynamics has a stronger effect on collective efficiency and equality of individual outcomes compared to a fear factor. Results of this study provide an initial description of strategy dynamics in engineering design and help to frame future work to mitigate potential unfavorable effects of their underlying strategy dynamics through social constructs or mechanism design.