An important result in convex analysis is the duality between a closed convex set and its support function. We exploit this duality to develop a novel geometric approach to mechanism design. For a general class of social choice problems we characterize the feasible set, which is closed and...

We consider a standard social choice environment with linear utilities and independent, one-dimensional, private values. We provide a short and constructive proof that for any Bayesian incentive compatible mechanism there exists an equivalent dominant strategy incentive compatible mechanism that...

Some labor markets have recently developed formal signalling mechanisms, e.g. the signalling for interviews in the job market for new Ph.D. economists. We evaluate the effect of such mechanisms on two-sided matching markets by considering a game of incomplete information between firms and...

We consider general social choice environments with private values and correlated types. Each agent's matrix of conditional probabilities satisfies the full rank condition. We show that for any Bayesian incentive compatible mechanism there exists a dominant strategy incentive compatible...

We introduce a simple two-stage game of endogenous network formation and information sharing for reasoning about the optimal design of social networks like Facebook or Google+. We distinguish between unilateral and bilateral connections and between targeted and collective information sharing....

We extend the equivalence between Bayesian and dominant strategy implementation established by Gershkov et al. (Econometrica, 2013) to environments with non-linear utilities satisfying the average single-crossing property and the convex-valued assumption. The new equivalence result produces...

For any linear transformation and two convex closed sets, we provide necessary and sufficient conditions for when the transformation of the intersection of the sets coincides with the intersection of their images. We also identify analogous conditions for non-convex sets, general...

We consider a model of monopolistic competition with several heterogeneous sectors and endogenous labor supply. For low (high) values of the labor supply elasticity, we show that there is always a unique equilibrium. For medium values of the labor supply elasticity, the set of equilibria (if...

We provide sufficient conditions for a monotone function with a finite set of outcomes to be cyclically monotone. Using these conditions, we show that any monotone function defined on the domain of gross substitutes is cyclically monotone. The result also extends to the domain of generalized...

A costless signaling mechanism has been proposed as a device to improve welfare in decentralized two-sided matching markets. An example of such an environment is a job market for new Ph.D. economists. We study a market game of incomplete information between firms and workers and show that...