Different markets are cleared by different types of prices -- seller-specific prices that are uniform across buyers in some markets, and personalized prices tailored to the buyer in others. We examine a setting in which buyers and sellers make investments before matching in a competitive market....

Different markets are cleared by different types of prices -- a universal price for all buyers and sellers in some markets, seller-specific prices that are uniform across buyers in others, and personalized prices tailored to both the buyer and the seller in yet others. We introduce the notion of...

We derive the existence of a Walras equilibrium directly from Nash's theorem on noncooperative games. No price player is involved, nor are generalized games. Instead we use a variant of the Shapley-Shubik trading-post game.