Related papers: Convexity and multi-dimensional screening for spac…
A monopolist seller of multiple goods screens a buyer whose type is initially unknown to both but drawn from a commonly known distribution. The buyer privately learns about his type via a signal. We derive the seller's optimal mechanism in…
One of the basic problems in discrete geometry is to determine the most efficient packing of congruent replicas of a given convex set $K$ in the plane or in space. The most commonly used measure of efficiency is density. Several types of…
We study the problem of fairly allocating indivisible goods and chores under category constraints. Specifically, there are $n$ agents and $m$ indivisible items which are partitioned into categories with associated capacities. An allocation…
In the Knapsack problem, one is given the task of packing a knapsack of a given size with items in order to gain a packing with a high profit value. An important connection to the $(\max,+)$-convolution problem has been established, where…
This paper examines the optimal contracts in a two-dimensional screening model where one dimension(group identity) is verifiable by agents but not falsifiable. A principal offers contracts to agents who differ in cost types and group…
We study a generalization of the knapsack problem with geometric and vector constraints. The input is a set of rectangular items, each with an associated profit and $d$ nonnegative weights ($d$-dimensional vector), and a square knapsack.…
This brief note considers the problem of learning with dynamic-optimizing principal-agent setting, in which the agents are allowed to have global perspectives about the learning process, i.e., the ability to view things according to their…
Let $n\geq 1$, $K>0$, and let $X=(X_1,X_2,\dots,X_n)$ be a random vector in $\mathbb{R}^n$ with independent $K$--subgaussian components. We show that for every $1$--Lipschitz convex function $f$ in $\mathbb{R}^n$ (the Lipschitzness with…
In this paper we study optimal advertising problems that models the introduction of a new product into the market in the presence of carryover effects of the advertisement and with memory effects in the level of goodwill. In particular, we…
We characterize optimal mechanisms for the multiple-good monopoly problem and provide a framework to find them. We show that a mechanism is optimal if and only if a measure $\mu$ derived from the buyer's type distribution satisfies certain…
We consider a general multi-agent convex optimization problem where the agents are to collectively minimize a global objective function subject to a global inequality constraint, a global equality constraint, and a global constraint set.…
A principal must decide between two options. Which one she prefers depends on the private information of two agents. One agent always prefers the first option; the other always prefers the second. Transfers are infeasible. One application…
We propose a distributionally robust principal agent formulation, which generalizes some common variants of worst-case and Bayesian principal agent problems. We construct a theoretical framework to certify whether any surjective contract…
We define in the space of n by m matrices of rank n, n less or equal than m, the condition Riemannian structure as follows: For a given matrix A the tangent space of A is equipped with the Hermitian inner product obtained by multiplying the…
Given an initial matching and a policy objective on the distribution of agent types to institutions, we study the existence of a mechanism that weakly improves the distributional objective and satisfies constrained efficiency, individual…
Finite-dimensional linear programs satisfy strong duality (SD) and have the "dual pricing" (DP) property. The (DP) property ensures that, given a sufficiently small perturbation of the right-hand-side vector, there exists a dual solution…
In the classical principal-agent problem, a principal must design a contract to incentivize an agent to perform an action on behalf of the principal. We study the classical principal-agent problem in a setting where the agent can be of one…
The class of assignment problems is a fundamental and well-studied class in the intersection of Social Choice, Computational Economics and Discrete Allocation. In a general assignment problem, a group of agents expresses preferences over a…
Linear contracts are ubiquitous in practice, yet optimal contract theory often prescribes complex, nonlinear structures. We provide a distributional robustness justification for linear contracts. We study a principal-agent problem where the…
The problem of computing near-optimal contracts in combinatorial settings has recently attracted significant interest in the computer science community. Previous work has provided a rich body of structural and algorithmic insights into this…