Nash Equilibrium Explains Why Billionaires Exist. New Pairing Structures for the “Prisoner’s Dilemma”

Nash Equilibrium allows for the analysis of a wide range of anthropological, economic, and psychological phenomena from a strictly logical perspective and with mathematical rigor. Nash proved that, in certain scenarios, all agents involved can make choices that are not the best, and yet it is not advantageous for them to change their decision. However, Nash’s original formulation only addresses the case in which individuals interact only once. The undue generalization of this solution to contexts with many agents and multiple interactions has generated misinterpretations with negative impacts on politics, economics, and other sectors, often resulting in significant waste of resources. In 1981 and 1984, tournaments conducted by Robert Axelrod showed that, in populations with varied profiles and numerous interactions, the most effective strategies are almost the opposite of those suggested by Nash. Since then, several studies have been conducted along the same lines, modifying parameters such as “number of agents”, “agent criteria”, “reward values”, etc. However, they did not explore changes in the structure of the pairing system, which are fundamental to understanding certain phenomena and to more faithfully reproducing the dynamics in real populations of living beings, especially complex human societies. In this article, we introduce a twofold methodological innovation: (a) new pairing structures that simulate partner selection in the real world and (b) a new metric capable of converting tournament scores into a scale that reflects inequalities of several orders of magnitude. The combined application of these tools reveals two crucial phenomena: first, the mechanism by which preferential cooperation amplifies inequality to levels compatible with the existence of billionaires; and second, how highly cooperative agents can become trapped in hostile environments due to the hermetic clustering that consolidates soon after the initial interactions, hindering social mobility, even when there are objective and measurable merits for advancement, a problem that requires urgent attention. notReviewed other