A Dichotomous Analysis of Unemployment Benefits

This paper introduces a novel framework for designing fair and sustainable unemployment 2 benefits, grounded in cooperative game theory and real-time fiscal policy. We conceptualize 3 the labor market as a coalitional game, where a random subset of individuals is employed, 4 generating stochastic economic output. To ensure fairness, we adopt equal employment 5 opportunity as a normative benchmark and introduce a dichotomous valuation rule that 6 assigns value to both employed and unemployed individuals. Within a continuous-time, 7 balanced budget framework, we derive a closed-form payroll tax rate that is fair, debt- 8 free, and asymptotically risk-free. This tax rule is robust across alternative objectives and 9 promotes employment, productivity, and equality of outcome. The framework naturally 10 extends to other domains involving random bipartitions and shared payoffs, such as voting 11 rights, health insurance, road tolling, and feature selection in machine learning. Our 12 approach offers a transparent, theoretically grounded policy tool for reducing poverty and 13 economic inequality while maintaining fiscal discipline.