Equilibrium Transition under Status-Quo Inertia: A Game-Theoretic Framework for Strategic Interventions in Family Conflict

Abstract Marriages sometimes collapse not through gradual erosion but through sudden, irreversible transitions after long periods of apparent stability. This paper develops a game-theoretic framework to analyze such critical transitions and to compare the effectiveness of different intervention strategies. We introduce the concept of statusquo inertia: an equilibrium selection rule that prioritizes the inherited equilibrium whenever it remains a Nash equilibrium after an intervention. Drawing on the intervention taxonomy of Eshaghi Gordji, Abounoori, and Berahman (2026), we distinguish price-only, addition, deletion, and replacement interventions. We show analytically that price-only and addition interventions are ineffective at changing outcomes whenever the status-quo equilibrium survives. Deletion interventions can destroy the old equilibrium but may leave coordination ambiguous. Replacement interventions—which remove a destructive action and simultaneously introduce a cooperative alternative—can both destroy the old equilibrium and create a focal efficient alternative. We analyze four canonical games (Prisoner’s Dilemma, Battle of the Sexes, Ultimatum Bargaining, and the Trust Game) that capture key marital conflicts and derive conditions under which replacement interventions induce equilibrium transition. Using detailed game matrices and transition diagrams, we demonstrate how replacing destructive actions with structured alternatives forces a transition to cooperative equilibria under plausible selection rules. Illustrative parallels from family law and mediation practices motivate the framework. The results provide testable predictions and offer a foundation for institutional design in contexts where status-quo inertia is strong.