Sustainable Exploitation Equilibria for Dynamic Games with Irreversible Failure
We study dynamic relationships in which one party extracts current surplus in ways that degrade the future state, while the counterparty cannot exit but adjusts effort in response. Standard stationary Markov equilibria may sustain collapse paths in which short-run extraction dominates strictly positive continuation gains. We introduce the Sustainable Exploitation Equilibrium (SEE), a refinement for dynamic games with irreversible failure modeled as an absorbing boundary that eliminates continuation value. When a survival-preserving action exists and failure destroys future surplus, equilibria assigning positive probability to collapse are sequentially irrational. Equilibrium analysis can therefore be restricted, without loss, to continuation-preserving stationary Markov equilibria. Within this restricted domain, viable renegotiation-proofness becomes structural: because failure truncates future surplus, any jointly improving survival-preserving deviation is credible prior to collapse. SEE selects the viable, renegotiation-stable equilibrium that maximizes the exploiter's value. Existence is established under standard conditions, and the refinement is illustrated in a hegemon-client setting.