Properties of switching-dynamics race models

Abstract

The paper analyses some continuous-time dynamic models that describe the evolution of social systems characterized by the possibility of changing the alliances among the parties involved or damaging one's competitors. At any time each participant, either an individual or a coalition, can decide to form or terminate a bond, or to start or stop damaging an opponent (i.e., to switch from a network configuration to another), based on a greedy, or shortsighted, criterion that does not consider the long-term effects of the decision. The proposed models fall within the domain of positive switching systems. Although they can obviously simulate the behaviour of many real-life situations, in which contenders aim at prevailing over one another to achieve supremacy, the paper does not refer to a specific context and concentrates on the main structural properties of the mathematical models, such as positivity and boundedness of the solutions, existence of coalitions, steady-state behaviour. Simulations show how the different cooperative or hostile attitudes of the participants affect their yield.