# A Geometric Approach to Mechanism Design

@article{Goeree2013AGA, title={A Geometric Approach to Mechanism Design}, author={Jacob K. Goeree and Alexey Kushnir}, journal={European Economics: Microeconomics \& Industrial Organization eJournal}, year={2013} }

We develop a novel geometric approach to mechanism design using an important result in convex analysis: the duality between a closed convex set and its support function. By deriving the support function for the set of feasible interim values we extend the wellknown Maskin-Riley-Matthews-Border conditions for reduced-form auctions to social choice environments. We next refine the support function to include incentive constraints using a geometric characterization of incentive compatibility…

## 19 Citations

### Ironing, Sweeping, and Multivariate Majorization Optimal Mechanisms for Mass-Produced Goods

- Economics
- 2020

We study the sale of an excludable, non-rival good by a monopolist when buyers’ values are interdependent, i.e. buyers’ utilities from consuming the good depend on their own and others’ information.…

### Uniform Graph and Foundations of Dominant-Strategy Mechanisms

- Economics
- 2015

An important question in mechanism design is whether there is any theoretical foundation for the use of dominant-strategy mechanisms. Following Chung and Ely (2007) who study maxmin and Bayesian…

### Greedy Allocations and Equitable Matchings

- Economics
- 2022

I study multi-item allocation problems when agents have capacity constraints. I ﬁrst provide an approximate extension to the multi-item setting of Border’s characterization of realizable interim…

### The Implementation Duality 1 Introduction

- Economics, Mathematics
- 2015

We use the theory of abstract convexity to study adverse-selection principal-agent problems and two-sided matching problems, departing from much of the literature by not requiring quasilinear…

### The Implementation Duality the Implementation Duality

- Economics, Mathematics
- 2015

We use the theory of abstract convexity to study adverse-selection principal-agent problems and two-sided matching problems, departing from much of the literature by not requiring quasilinear…

### Incentive Compatibility with Non-Convex Type Spaces∗

- Economics, Mathematics
- 2021

We present results concerning the incentive compatibility of mechanisms when the agent’s type space may not be convex. In particular, we provide a necessary condition for incentive compatibility when…

### On the Equivalence between Bayesian and Dominant Strategy Implementation: The Case of Correlated Types

- Economics
- 2013

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…

### Understanding Preferences: “Demand Types”, and the Existence of Equilibrium With Indivisibilities

- EconomicsEconometrica
- 2019

An Equivalence Theorem between geometric structures and utility functions allows new methods for understanding preferences. Our classification of valuations into “Demand Types” incorporates existing…

### Extreme Points and Majorization: Economic Applications

- Economics, MathematicsEconometrica
- 2021

We characterize the set of extreme points of monotonic functions that are either majorized by a given function
f or themselves majorize
f and show that these extreme points play a crucial role in…

## References

SHOWING 1-10 OF 97 REFERENCES

### Multidimensional Mechanism Design: Finite-Dimensional Approximations and Efficient Computation

- MathematicsOper. Res.
- 2010

It is illustrated how the numerical solutions of the finite-dimensional approximations can provide insights into the nature of optimal solutions to the infinite-dimensional problem in particular cases.

### Optimal Multi-dimensional Mechanism Design: Reducing Revenue to Welfare Maximization

- Economics2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
- 2012

The results are computationally efficient for all multidimensional settings where the bidders are additive, or can be efficiently mapped to be additive, albeit the feasibility and demand constraints may still remain arbitrary combinatorial.

### Multidimensional Mechanism Design: Revenue Maximization and the Multiple-Good Monopoly

- EconomicsJ. Econ. Theory
- 2007

A simple algebraic procedure is provided to determine whether a mechanism is an extreme point of the feasible set, which maximizes revenue for a well-behaved distribution of buyer’s valuations.

### An algorithmic characterization of multi-dimensional mechanisms

- EconomicsSTOC '12
- 2012

The results provide a characterization of feasible, Bayesian Incentive Compatible mechanisms in multi-item multi-bidder settings, and give a proper generalization of Border's Theorem for a broader class of feasibility constraints, including the intersection of any two matroids.

### Robust Mechanism Design

- Economics
- 2003

The mechanism design literature assumes too much common knowledge of the environment among the players and planner. We relax this assumption by studying implementation on richer type spaces, with…

### Bayesian optimal auctions via multi- to single-agent reduction

- EconomicsEC '12
- 2012

An abstract optimal auction problem for selecting a subset of self-interested agents to whom to provide a service, and shows that interim feasible allocation rules can be optimized over and implemented via a linear program that has quadratic complexity in the sum of the sizes of the individual agents' type spaces.

### Automated Design of Revenue-Maximizing Combinatorial Auctions

- Computer ScienceOper. Res.
- 2015

Algorithms that design high-revenue CAs for general valuations using samples from the prior distribution over bidders’ valuations are developed, and properties of the problem that guide the design of algorithms are proved.

### Auction Design with Fairness Concerns: Subsidies vs. Set-Asides

- Economics
- 2012

Government procurement and allocation programs often use subsidies and set-asides favoring small businesses and other target groups to address fairness concerns. These concerns are in addition to…

### A general characterization of interim efficient mechanisms for independent linear environments

- EconomicsJ. Econ. Theory
- 2007