Large contests without single crossing

We show that the equilibria of contests with many players and prizes are approximated by certain single-agent mechanisms. This complements the work of Olszewski and Siegel (Econometrica 84:835–854, 2016), who considered a more restricted environment in which players’ utility function satisfies a strict single crossing condition. Relaxing strict single crossing enlarges the set of approximating mechanisms and weakens the notion of approximation, but implications regarding equilibrium behavior in large contests can nevertheless often be derived. When the approximating mechanism is unique, a stronger notion of approximation obtains.