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Ensuring sufficient liquidity is one of the key challenges for designers of prediction markets. Various market making algorithms have been proposed in the literature and deployed in practice, but there has been little effort to evaluate…
Competitive equilibrium is a central concept in economics with numerous applications beyond markets, such as scheduling, fair allocation of goods, or bandwidth distribution in networks. Computation of competitive equilibria has received a…
We propose a pseudo-market solution to resource allocation problems subject to constraints. Our treatment of constraints is general: including bihierarchical constraints due to considerations of diversity in school choice, or scheduling in…
In this paper we study two-player bilinear zero-sum games with constrained strategy spaces. An instance of natural occurrences of such constraints is when mixed strategies are used, which correspond to a probability simplex constraint. We…
We introduce robust learning equilibrium. The idea of learning equilibrium is that learning algorithms in multi-agent systems should themselves be in equilibrium rather than only lead to equilibrium. That is, learning equilibrium is immune…
We propose an enhancement to Benders decomposition (BD) that generates valid inequalities for the convex hull of the Benders reformulation, addressing the limitation that classical BD cuts are typically tight only for the continuous…
A major goal in Algorithmic Game Theory is to justify equilibrium concepts from an algorithmic and complexity perspective. One appealing approach is to identify robust natural distributed algorithms that converge quickly to an equilibrium.…
With a Bayesian approach, the linear optics correction algorithm for storage rings is revisited. Starting from the Bayes' theorem, a complete linear optics model is simplified as "likelihood functions" and "prior probability distributions".…
The aim of this article is to introduce an iterative algorithm for finding a common solution from the set of an equilibrium point for a bifunction and the set of a singularity of an inclusion problem on an Hadamard manifold. We also discuss…
Advances in computational optimization allow for the organization of large combinatorial markets. We aim for allocations and competitive equilibrium prices, i.e. outcomes that are in the core. The research is motivated by the design of…
Calibration of neural networks is a topical problem that is becoming more and more important as neural networks increasingly underpin real-world applications. The problem is especially noticeable when using modern neural networks, for which…
Many challenging tasks in sensor networks, including sensor calibration, ranking of nodes, monitoring, event region detection, collaborative filtering, collaborative signal processing, {\em etc.}, can be formulated as a problem of solving a…
We consider class of equilibrium models including the implicit Walras supply-demand and competitive models. Such a model in this class, in general, is ill-posed. We formulate such a model in the form a variational inequality having certain…
This manuscript proposes a probabilistic framework for algorithms that iteratively solve unconstrained linear problems $Bx = b$ with positive definite $B$ for $x$. The goal is to replace the point estimates returned by existing methods with…
We propose a new methodology to compute equilibria for general equilibrium problems on exchange economies with real financial markets, home-production, and retention. We demonstrate that equilibrium prices can be determined by solving a…
We study the question of extracting a sequence of functions $\{\boldsymbol{f}_i, \boldsymbol{g}_i\}_{i=1}^s$ from observing only the sum of their convolutions, i.e., from $\boldsymbol{y} = \sum_{i=1}^s \boldsymbol{f}_i\ast…
A natural optimization model that formulates many online resource allocation and revenue management problems is the online linear program (LP) in which the constraint matrix is revealed column by column along with the corresponding…
Selling a perfectly divisible item to potential buyers is a fundamental task with apparent applications to pricing communication bandwidth and cloud computing services. Surprisingly, despite the rich literature on single-item auctions,…
We consider the disjoint bilinear programming problem in which one of the disjoint subsets has the structure of an acute-angled polytope. An optimality criterion for such a problem is formulated and proved, and based on this, a polynomial…
The linearized Bregman iterations (LBreI) and its variants are powerful tools for finding sparse or low-rank solutions to underdetermined linear systems. In this study, we propose a cut-and-project perspective for the linearized Bregman…