Binary or nonbinary? An evolutionary learning approach to gender identity

Is gender identity binary or nonbinary? My analysis shows that while both are possible, the latter is a more attracting equilibrium under an adaptive learning perspective. I frame the gender identity problem as a modified \textit{battle of the sexes} game, where individuals define their gender identity under pairwise matching motives. From a baseline game-theoretical standpoint, I demonstrate that the binary-only world and the nonbinary-only world are both Nash equilibria in the stage game and are locally stable in the infinitely repeated game. Thus, any state of gender identity could theoretically persist. I then adopt a genetic learning algorithm as an equilibrium selection criterion to investigate evolutionary dynamics further and provide a rationale for the transition from binary to nonbinary gender identity. Specifically, in a binary-origin world, divergence occurs as individuals identifying as nonbinary gender evolve to become the majority due to their higher flexibility in matching outcomes. My framework captures how adaptive learning drives identity evolution, offering a parsimonious tool to analyze how diversity and exclusivity emerge in varying economic environments.