Endogenous Agreement Geometry in Nash Bargaining over a Continuum of Issues

Many bargaining problems allocate control over heterogeneous issues rather than a single scalar surplus. This paper studies a two-player game-theoretic Nash bargaining problem over a continuum of issues with stochastic valuation fields. Taking the classical maximum Nash welfare cutoff allocation as a benchmark, we characterize the selected agreement as an endogenous excursion set of the log-relative valuation field. We then study its economic geometry: stationarity and ergodicity yield deterministic many-issue payoff limits, a finite-domain perturbation formula separates local shocks from global cutoff feedback, Kac–Rice methods describe boundary intensity, and a perimeter penalty for fragmented contracts turns the bargain into a finite perimeter variational problem. At regular boundary points, the complexity-penalized bargain satisfies a curvature-adjusted bargaining condition. The analysis connects cooperative game theory, Nash bargaining, fair division, random field geometry, and contract complexity.