Strategic Identity Equilibrium: Redefining the Agent in Game Theory

We introduce Strategic Identity Equilibrium (SIE), a generalization of game-theoretic rationality in which agents select strategies not only to maximize expected utility, but to stabilize internal coherence. In contrast to classical models—which assume fully formed agents with fixed preferences—SIE models the agent as a structure in flux, shaped by role conflict, identity dynamics, and coherence thresholds.In this framework, a strategy is viable only if it satisfies both external payoff considerations and internal structural alignment. We formally define SIE, prove its existence, and demonstrate that it contains Nash Equilibrium, Quantal Response Equilibrium, and Bayesian learning as limiting cases.Unlike these models, SIE predicts strategy dropout, cycling, delayed convergence, and identity-driven nonselection—behaviors often dismissed as noise in classical theory. We provide behavioral scenarios, falsifiability criteria, and estimation proxies to enable experimental and simulation-based testing. Applications range from coordination and cooperation to polarization, institutional collapse, and multi-agent systems.By redefining the agent as a coherence-seeking structure, SIE offers a rigorous and testable foundation for modeling strategic behavior that is not only rational—but recognizably human.