Matemáticas sociales y estructuras del liberalismo: teoría de juegos e hipergrafos

abstract. the main results of social mathematics were inspired by the liberal economical and political ideas that started to prevail in the 18th century. this review focuses on theorems that reveal the limitations of liberalism. to organize collaboration, this social paradigm recommends negotiated solutions. but to ensure the existence of such equilibrium, the action domains may need to be restricted. structures have to be imposed that typically favor rich and powerful agents. even so, they cannot avoid economical situations in which the entailed equilibrium turns out to be very disappointing for everybody. such paradoxical situations can be solved only if, due to solidarity commitments, the agents can trust each other. the review also comments on attitudes and considerations that should orient the practice of social mathematics.