Dynamics of Two-Actor Cooperation-Competition Conflict Models

A mathematical model for conflict can give us insight into which mechanisms are the most important in maintaining or resolving a conflict. We developed a nonlinear model of the interactions in time between two groups based on the intuitive and experimental insights of Deustch (1973, 2006) and Pruitt (1969, 2006) and the dynamical insights of Gottman, Murray, Swanson, Tyson, and Swanson (2002) and Coleman, Vallacher, Nowak, and Bui-Wrzosinska (2006). In this model, the state of each group at a given moment in time depends on its own state in isolation, its previous state in time, its inertia to change, and the influence from the other group. Each group can influence the other group either through cooperation, that is positive feedback, or through competition, that is negative feedback. We analyzed this model using analytical methods and numerical computer simulations. We show how the positive or negative feedback between the groups leads to different dynamics and steady states. When the strength of the feedback is less than the inertia to change, then positive or negative feedback between both groups leads both groups into a neutral state. Above this threshold their behavior changes. Positive feedback between both groups leads to either both groups being in a positive state or both groups being in a negative state. Negative feedback between both groups leads to both groups being neutral or in opposite positive and negative states. Whether they are both neutral or in opposite states depends sensitively on their initial states and their uninfluenced states which tips their behavior from being neutral into entirely new states. Mixed negative and positive feedback between the groups results in oscillations between positive and negative states with both groups stabilizing in a neutral state. These results give us insight into how the dynamics of group behavior depends on the cooperation or competition between the groups