There have been major disputes about the appropriate game-theoretic analyses of sports leagues. The basic sports-league model assumes a two-team league where each team is seen as a monopolist in its product market and a passive price taker in a duopsony talent market. For simplicity, these models assume talent supply is either perfectly inelastic or perfectly elastic. It has been argued that perfectly inelastic supply is ill suited for duopsony analysis. This article solves the problem of multiple equilibria by proposing a selection criterion that finds a unique equilibrium in a duopsony limit game as talent supply approaches perfect inelasticity.