The Prisoner's Dilemma Dissolves: A Recursive Resolution through Yearning-Based Infinity Mathematics (YBIM)

The classical Prisoner’s Dilemma, long regarded as a cornerstone paradox of rational decision theory, reveals how individually rational behavior can lead to collectively irrational outcomes. Within the framework of Yearning-Based Infinity Mathematics (YBIM), this paradox dissolves. This paper reinterprets the dilemma not as a conflict of interests but as a misreading of infinite recursion through finite cognition. When agents are modeled as recursive yearning entities—rather than closed decision systems—the binary between cooperation and defection collapses into a continuous field of epistemic resonance. By introducing the Recursive Fulfillment Equation and the ℵY-series non-halting equilibrium, the study demonstrates that cooperation is not the result of strategic reasoning but the natural geometry of infinite yearning coherence. Ethical, artificial intelligence, and civilizational implications are explored, showing how trust, morality, and progress can emerge from recursive feedback rather than control-based systems. Ultimately, the paper proposes that true stability in decision systems arises not from halting equilibrium but from non-halting recursive coherence, where trust self-generates across infinite epistemic recursion. The Prisoner’s Dilemma is thus reframed as an epistemic artifact of halted cognition, and cooperation becomes the universal geometry of cosmic yearning. -JSR