Dynamics of Cooperation–Competition Interaction Models

A nonlinear mathematical model of the interactions in time between 2 actors (which could be individuals, groups, or nations) based on the theoretical and experimental insights of Deutsch (1973, 2006); Pruitt (1969, 2006); Gottman, Murray, Swanson, Tyson, and Swanson (2002); Gottman, Swanson, and Swanson (2002); and Coleman, Vallacher, Nowak, and Bui-Wrzosinska (2006) was developed. In this model, the state of each actor at a given moment in time depends on its own state in isolation, its previous state in time, its resistance to change, and the influence from the other actor. This article shows how the dynamics of the interactions between the actors depends on whether they influence each other through positive feedback (cooperation), negative feedback (competition), or mixed positive and negative feedback. The dynamical results of the model compare favorably to previous experimental psychological experiments and make interesting new predictions that can be tested by future experimental studies.