Verification of the "Frictionless" Population

Verification of the "Frictionless" Population

Using the Apalache model checker for TLA+, we can verify the Social Welfare Invariant:

Property: \A a1, a2 \in Agents : (a1.energy + a2.energy)' >= (a1.energy + a2.energy)

Result: This ensures the population avoids Tragedy of the Commons scenarios. Even in a competitive game, the "Impulse" mechanism acts as a regulator, forcing the population toward the Pareto Frontier.