Related papers: A primal-dual price-optimization method for comput…
Variational inequality problems are recognized for their broad applications across various fields including machine learning and operations research. First-order methods have emerged as the standard approach for solving these problems due…
In this paper, we present an efficient algorithm for solving a linear optimization problem with entropic constraints, a class of problems that arises in game theory and information theory. Our analysis distinguishes between the cases of…
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…
We consider the setting of agents cooperatively minimizing the sum of local objectives plus a regularizer on a graph. This paper proposes a primal-dual method in consideration of three distinctive attributes of real-life multi-agent…
We formulate and investigate a mean field optimization (MFO) problem over a set of probability distributions $\mu$ with a prescribed marginal $m$. The cost function depends on an aggregate term, which is the expectation of $\mu$ with…
The linear primal-dual hybrid gradient (PDHG) method is a first-order method that splits convex optimization problems with saddle-point structure into smaller subproblems. Unlike those obtained in most splitting methods, these subproblems…
Recently, there is growing interest and need for dynamic pricing algorithms, especially, in the field of online marketplaces by offering smart pricing options for big online stores. We present an approach to adjust prices based on the…
In this work, we show that for linearly constrained optimization problems the primal-dual hybrid gradient algorithm, analyzed by Chambolle and Pock [3], can be written as an entirely primal algorithm. This allows us to prove convergence of…
Traditional solvable game theory and mean-field-type game theory (risk-aware games) predominantly focus on quadratic costs due to their analytical tractability. Nevertheless, they often fail to capture critical non-linearities inherent in…
In revenue maximization of selling a digital product in a social network, the utility of an agent is often considered to have two parts: a private valuation, and linearly additive influences from other agents. We study the incomplete…
Predatory pricing -- where a firm strategically lowers prices to undermine competitors -- is a contentious topic in dynamic oligopoly theory, with scholars debating practical relevance and the existence of predatory equilibria. Although…
We study the optimal mechanism design problem faced by a market intermediary who makes revenue by connecting buyers and sellers. We first show that the optimal intermediation protocol has substantial structure: it is the solution to an…
We introduce a criterion how to price derivatives in incomplete markets, based on the theory of growth optimal strategy in repeated multiplicative games. We present reasons why these growth-optimal strategies should be particularly relevant…
We consider the problem of supply and demand balancing that is stated as a minimization problem for the total expected revenue function describing the behavior of both consumers and suppliers. In the considered market model we assume that…
We compute equilibrium strategies in multi-stage games with continuous signal and action spaces as they are widely used in the management sciences and economics. Examples include sequential sales via auctions, multi-stage elimination…
This paper proposes a new mathematical paradigm to analyze discrete-time mean-field games. It is shown that finding Nash equilibrium solutions for a general class of discrete-time mean-field games is equivalent to solving an optimization…
Necessary optimality conditions in Lagrangian form and the sequential minimization framework are extended to mixed-integer nonlinear optimization, without any convexity assumptions. Building upon a recently developed notion of local…
We introduce a new framework for optimal routing and arbitrage in AMM driven markets. This framework improves on the original best-practice convex optimization by restricting the search to the boundary of the optimal space. We can…
This study investigates an adaptive pricing scheme aimed at achieving an efficient state in a traffic congestion game characterized by a diverse population of road users. While the planner possesses knowledge of players' preferences, their…
We consider the classical mathematical economics problem of {\em Bayesian optimal mechanism design} where a principal aims to optimize expected revenue when allocating resources to self-interested agents with preferences drawn from a known…