Asymmetric Outcomes in Two-Actor Conflict Dynamics: Stability, Bifurcations, and Emergent Behaviors

In this paper we present an analytical and numerical study of a generalized model of two-actor cooperative-competitive conflict of the Continuous Opinions and Discrete Actions (CODA) type. Theoretically, we note that the in troduction of a new parameter allows generalizing feedback as strong and weak. Furthermore, we show that for positive-positive and negative-negative feedback there exists a supercritical pitchfork bifurcation, and that the model does not admit limit cycles in any case, and we study the effect of different parameter values and initial conditions by using a difference equation approximation of the model. Additionally, our model offers important insight on social phenomena such as false levels of support among cooperators, often observed in agreement negotiations; instances of ``non-strict consensus'' when two people support the same political position, albeit with different intensities; and competitive situations, such as in competitions with disproportionate profit and losses. Thus, this generalized model offers an enhanced descriptive power compared to previously proposed models.