The ∆-Equilibrium: Equilibrium Exists Only in Alive Markets (No Equilibrium in Dead State)

We present ∆-Equilibrium a self-contained equilibrium equilibrium with no externaland no internal assumptions. We build on Zulfia Frame ∆η(x, u) = 0, η ∈ ∆, whichis ZIC common base [1].We establish that equilibrium exists only for alive markets where deviation∆(x∗)̸ = 0 and ZIC ∆η(x∗, u) = 0 holds, while no equilibrium exists for dead statewhere ∆(x∗) = 0.We demonstrate applications to dual factory-swamp economy, informal credit,and P2P markets, where classical equilibrium fails when assumed state xS0 vanishes,but our equilibrium persists as long as market is alive.