The Mathematics of Aggregation, Interdependence, Organizations and Systems of Nash Equilibria: A Replacement for Game Theory

Traditional social science research has been unable to satisfactorily aggregate individual level data to group, organization and systems levels, making it one of social science’s biggest challenges (Giles, 2011). For game and social theory, we believe that the fault can be attributed to the lack of valid distance measures (e.g., the arbitrary ordering of cooperation and competition precludes a Hilbert space distance metric for the ordering of and gradations between these social behaviors, making game theory normative). Alternatively, we offer a theory of social interdependence with countable mathematics based on bistable or multi-stable perspectives and linear algebra. The evidence that is available is supportive. It indicates that meaning is a one-sided, stable, classical interpretation, not only making the correspondence between beliefs and objective reality in social settings incomplete, raising questioning about static theories from earlier eras (i.e., Axelrod’s evolution of cooperation; Simon’s bounded rationality). The result indicates for open systems (democracies) that interpretations evolve naturally to become orthogonal (Nash equilibria), that orthogonal interpretations generate the information to drive social evolution, but that in closed systems (dictatorships), dependent on the enforcement of social cooperation and the suppression of opposing points of view, evolution slows or stops (e.g., China, Iran or Cuba), causing capital and energy to be wasted, misdirected or misallocated as leaders suppress the interpretations that they alone have the authority to label as unethical, immoral, or irreligious. We conclude that a mathematics based on NE is feasible.