Properties of switching-dynamics race models

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.