Riley (1979)'s reactive equilibrium concept addresses problems of equilibrium existence in competitive markets with adverse selection. The game-theoretic interpretation of the reactive equilibrium concept in Engers and Fernandez (1987) yields the Rothschild-Stiglitz (1976)/Riley (1979)...

We provide a shorter proof of the main result in Reny and Perry (2006, Econometrica) by establishing a lower semicontinuity property of auctions as the number of traders goes to infinity, leveraging existence of equilibria in the limit auction. Our proof also eliminates two of the assumptions in...