Related papers: Application of Coupled Fixed (or Best Proximity) P…
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…
This paper provides a general mathematical optimization based framework to incorporate fairness measures from the facilities' perspective to Discrete and Continuous Maximal Covering Location Problems. The main ingredients to construct a…
The goal of an auction is to determine commodity prices such that all participants are perfectly happy. Such a solution is called a competitive equilibrium and does not exist in general. For this reason we are interested in solutions which…
In this paper, we extend and improve the production chain model introduced by Kikuchi et al. (2018). Utilizing the theory of monotone concave operators, we prove the existence, uniqueness, and global stability of equilibrium price, hence…
In this paper, we consider solving a composite optimization problem with coupling constraints in a multi-agent network based on proximal gradient method. In this problem, all the agents jointly minimize the sum of individual cost functions…
One attractive approach to market dynamics is the level $k$ model in which a level $0$ player adopts a very simple response to current conditions, a level $1$ player best-responds to a model in which others take level $0$ actions, and so…
Minimax optimization has become a central tool in machine learning with applications in robust optimization, reinforcement learning, GANs, etc. These applications are often nonconvex-nonconcave, but the existing theory is unable to identify…
Multiobjective combinatorial optimization deals with problems considering more than one viewpoint or scenario. The problem of aggregating multiple criteria to obtain a globalizing objective function is of special interest when the number of…
This working paper is divided into two parts. Firstly, we develop a new combined equilibrium model of business land-use, which puts travelers' traffic equilibrium and business companies' competitive location equilibrium into a unified…
What is the performance cost of using simple, decoupled control policies in inherently coupled systems? Motivated by industrial refrigeration systems, where centralized compressors exhibit economies of scale yet traditional control employs…
We use a method of Luczak (arXiv:1212.3231) to investigate the equilibrium distribution of a dynamic routing model on a network. In this model, there are $n$ nodes, each pair joined by a link of capacity $C$. For each pair of nodes, calls…
For two nonempty, closed, bounded and convex subsets $A$ and $B$ of a uniformly convex Banach space $X$ consider a mapping $T:(A \times B) \cup (B \times A) \rightarrow A \cup B$ satisfying $T(A,B) \subset B$ and $T(B, A) \subset A$. In…
Equilibrium computation in markets usually considers settings where player valuation functions are known. We consider the setting where player valuations are unknown; using a PAC learning-theoretic framework, we analyze some classes of…
The paper discusses the conditions for the existence of fixed points of multivalued mappings that are not based on the linear structure of the set. The descriptions for the sets of fixed points for mappings with closed graph in compact…
Many models from a variety of areas involve the computation of an equilibrium or fixed point of some kind. Examples include Nash equilibria in games; market equilibria; computing optimal strategies and the values of competitive games…
We propose a model of incentives for data pricing in large mobile networks, in which an operator wishes to balance the number of connections (active users) of different classes of users in the different cells and at different time instants,…
This paper investigates the synthesis of distributed economic control algorithms under which dynamically coupled physical systems are regulated to a variational equilibrium of a constrained convex game. We study two complementary cases: (i)…
European Member States are increasingly introducing national capacity mechanisms (CMs) to manage growing adequacy risks. However, isolated national CMs are inefficient in highly interconnected electricity systems, such as the European…
We study the problem of collaborative machine learning markets where multiple parties can achieve improved performance on their machine learning tasks by combining their training data. We discuss desired properties for these machine…
In the Normed space theory, the existence of fixed points is one of the main tools in improving efficiency of iterative algorithms in optimization, numerical analysis and various mathematical applications. This study introduces and…