We define a standard optimization problem with quadratic objective function and provide a rigorous visual proof for its solution without using calculus. We then show that such standard problem is a building block for several economic models related to microeconomics, game theory and pricing...

We consider an exchange economy in which a seller can trade an endowment of a divisible good whose quality she privately knows. Buyers compete in menus of non-exclusive contracts, so that the seller may choose to trade with several buyers. In this context, we show that an equilibrium always...

This paper examines the role of the revelation principle in common agency games. We show how the introduction of a separability condition on the preferences of the agent is sufficient for the revelation principle to hold. Therefore, it is still possible to restrict attention to direct mechanisms...

We consider Common Agency games of moral hazard and we suggest that there is only a very weak support for the standard restriction to take-it or leave-it contracts.

A seller of a divisible good faces several identical buyers. The quality of the good may be low or high, and is the seller's private information. The seller has strictly convex preferences that satisfy a single-crossing property. Buyers compete by posting menus of nonexclusive contracts, so that...

We study a discriminatory limit-order book in which market makers compete in nonlinear tariffs to serve a privately informed insider. Our model allows for general nonparametric specifications of preferences and arbitrary discrete distributions for the insider's private information. Adverse...

We study resource allocation under private information when the planner cannot prevent bilateral side trading between consumers and firms. Adverse selection and side trading severely restrict feasible trades: each marginal quantity must be fairly priced given the consumer types who purchase it....