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We consider the convex bilevel optimization problem, also known as simple bilevel programming. There are two challenges in solving convex bilevel optimization problems. Firstly, strong duality is not guaranteed due to the lack of Slater…
Many interesting problems in the Internet industry can be framed as a two-sided marketplace problem. Examples include search applications and recommender systems showing people, jobs, movies, products, restaurants, etc. Incorporating…
We study the power of price discrimination via an intermediary in bilateral trade, when there is a revenue-maximizing seller selling an item to a buyer with a private value drawn from a prior. Between the seller and the buyer, there is an…
Given a convex optimization problem and its dual, there are many possible first-order algorithms. In this paper, we show the equivalence between mirror descent algorithms and algorithms generalizing the conditional gradient method. This is…
We provide a model-free pricing-hedging duality in continuous time. For a frictionless market consisting of $d$ risky assets with continuous price trajectories, we show that the purely analytic problem of finding the minimal superhedging…
Market price systems constitute a well-understood class of mechanisms that under certain conditions provide effective decentralization of decision making with minimal communication overhead. In a market-oriented programming approach to…
How to compute (super) hedging costs in rather general fi- nancial market models with transaction costs in discrete-time ? Despite the huge literature on this topic, most of results are characterizations of the super-hedging prices while it…
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
Competition is a main tenet of economics, and the reason is that a perfectly competitive equilibrium is Pareto-efficient in the absence of externalities and public goods. Whether a product is selected in a market crucially relates to its…
The design of energy markets is a subject of ongoing debate, particularly concerning the choice between the widely adopted Pay-as-Clear (PC) pricing mechanism and the alternative Pay-as-Bid (PB). These mechanisms determine how energy…
In this paper we consider a distributed optimization scenario in which a set of agents has to solve a convex optimization problem with separable cost function, local constraint sets and a coupling inequality constraint. We propose a novel…
Using duality theory techniques we derive simple, closed-form formulas for bounding the optimal revenue of a monopolist selling many heterogeneous goods, in the case where the buyer's valuations for the items come i.i.d. from a uniform…
We consider a revenue maximization model, in which a company aims at designing a menu of contracts, given a population of customers. A standard approach consists in constructing an incentive-compatible continuum of contracts, i.e., a menu…
We study the problem of designing a two-sided market (double auction) to maximize the gains from trade (social welfare) under the constraints of (dominant-strategy) incentive compatibility and budget-balance. Our goal is to do so for an…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
We investigate the links between various no-arbitrage conditions and the existence of pricing functionals in general markets, and prove the Fundamental Theorem of Asset Pricing therein. No-arbitrage conditions, either in this abstract…
Currently, most ISOs adopt offer cost minimization (OCM) auction mechanism which minimizes the total offer cost, and then, a settlement rule based on either locational marginal prices (LMPs) or market clearing price (MCP) is used to…
Price differentiation is a common strategy in many markets. In this paper, we study a static multiproduct price optimization problem with demand given by a discrete mixed multinomial logit model. By considering a mixed logit model that…
Motivated by the increasing integration among electricity markets, in this paper we propose two different methods to incorporate market integration in electricity price forecasting and to improve the predictive performance. First, we…
A multi-product monopolist faces a buyer who is privately informed about his valuations for the goods. As is well-known, optimal mechanisms are in general complicated, while simple mechanisms -- such as pure bundling or separate sales --…