Related papers: A primal-dual price-optimization method for comput…

In this paper, we propose a mean-field game model for the price formation of a commodity whose production is subjected to random fluctuations. The model generalizes existing deterministic price formation models. Agents seek to minimize…

In this work, we revisit a classical incremental implementation of the primal-descent dual-ascent gradient method used for the solution of equality constrained optimization problems. We provide a short proof that establishes the linear…

We consider a market where a finite number of players trade an asset whose supply is a stochastic process. The price formation problem consists of finding a price process that ensures that when agents act optimally to minimize their trading…

In this paper, we consider a large class of hierarchical congestion population games. One can show that the equilibrium in a game of such type can be described as a minimum point in a properly constructed multi-level convex optimization…

Large-scale competitive market equilibrium problems arise in a wide range of important applications, including economic decision-making and intelligent manufacturing. Traditional solution methods, such as interior-point algorithms and…

We present a general technique, based on a primal-dual formulation, for analyzing the quality of self-emerging solutions in weighted congestion games. With respect to traditional combinatorial approaches, the primal-dual schema has at least…

Here, we examine a fully-discrete Semi-Lagrangian scheme for a mean-field game price formation model. We show the existence of the solution of the discretized problem and that it is monotone as a multivalued operator. Moreover, we show that…

Designing an incentive compatible auction that maximizes expected revenue is a central problem in Auction Design. While theoretical approaches to the problem have hit some limits, a recent research direction initiated by Duetting et al.…

We propose a machine learning method to solve a mean-field game price formation model with common noise. This involves determining the price of a commodity traded among rational agents subject to a market clearing condition imposed by…

An universal primal-dual approach of description equilibriums in large class of hierarchical congestion population games is proposed. At the very core of the approach is hierarchy of enclosed to each other transport networks. In different…

The paper studies a distributed constrained optimization problem, where multiple agents connected in a network collectively minimize the sum of individual objective functions subject to a global constraint being an intersection of the local…

In the literature, existence of mean-field equilibria has been established for discrete-time mean field games under both the discounted cost and the average cost optimality criteria. In this paper, we provide a value iteration algorithm to…

In this work, we study an equilibrium-based continuous asset pricing problem which seeks to form a price process endogenously by requiring it to balance the flow of sales-and-purchase orders in the exchange market, where a large number of…

We consider the resource allocation problem and its numerical solution. The following constructions are demonstrated: 1) Walrasian price-adjustment mechanism for determining the equilibrium; 2) Decentralized role of the prices; 3) Slater's…

We propose the concept of a Lagrangian game to solve constrained Markov games. Such games model scenarios where agents face cost constraints in addition to their individual rewards, that depend on both agent joint actions and the evolving…

The presence of integer variables in the European day-ahead electricity market renders the social welfare maximization problem non-convex and non-differentiable, making classical marginal pricing theoretically inconsistent. Existing pricing…

This paper is devoted to finite horizon deterministic mean field games in which the state space is a network. The agents control their velocity, and when they occupy a vertex, they can enter into any incident edge. The running and terminal…

By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…

In settings where full incentive-compatibility is not available, such as core-constraint combinatorial auctions and budget-balanced combinatorial exchanges, we may wish to design mechanisms that are as incentive-compatible as possible. This…

In this paper, we introduce a novel first-order dual gradient algorithm for solving network utility maximization problems that arise in resource allocation schemes over networks with safety-critical constraints. Inspired by applications…