Thermodynamics of Cooperation: Cooperative Equilibrium

We prove that in a repeated multi-agent game with energy-denominated payoffs derived from thermodynamic first principles, universal cooperation is the unique Nash equilibrium that simultaneously satisfies Pareto efficiency and welfare maximization. The payoff matrix is not stipulated but constructed from physical parameters (resource energy, friction multipliers, exploitation efficiency, and repair costs), yielding a Prisoner's Dilemma in which mutual defection is net-negative ($P < 0$) rather than merely suboptimal. This structural property drives the cooperation threshold to $\delta^* = 0.363$, substantially below the canonical $0.5$. We prove that defection is evolutionarily unstable, self-extinguishing in friction-coupled networks, and unprofitable even from a single deviation when network effects are included. The friction state variable, encoding the cumulative memory of past violations, enters payoffs endogenously, making punishment self-reinforcing without external enforcement. We explicitly characterize the relationship between these results and established repeated-game theory: the known machinery is the Folk Theorem and ESS analysis; the novel content is the derived payoff matrix, structurally negative mutual defection, equilibrium selection, and endogenous persistent friction.