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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…
In the early $20^{th}$ century, Pigou observed that imposing a marginal cost tax on the usage of a public good induces a socially efficient level of use as an equilibrium. Unfortunately, such a "Pigouvian" tax may also induce other,…
We analyze analytically the effect of congestion costs within a physically relevant, yet exactly solvable network model featuring central hubs. These costs lead to a competition between centralized and decentralized transport pathways. In…
We described the average traffic congestion in several populous cities around the world from a new concept, namely landscape percolation. The ratio of the residential area size to road width is a fundamental parameter that controls the…
We consider the efficient outcome of a canonical economic market model involving buyers and sellers with independent and identically distributed random valuations and costs, respectively. When the number of buyers and sellers is large, we…
We present a simple discrete model for the non-linear spatial interaction of different kinds of ``subpopulations'' composed of identical moving entities like particles, bacteria, individuals, etc. The model allows to mimic a variety of…
We study the joint control of arrival and service rates in queueing systems with the objective of minimizing long-run expected cost minus revenue. Although the objective function is non-convex, first-order methods have been empirically…
Natural flocks (aligned) and swarms (non-aligned) both exhibit features of near-criticality, challenging their treatment as two ends of the same phase transition. We present a model for the aggregation of active individuals, in which their…
We study Markov decision processes with Polish state and action spaces. The action space is state dependent and is not necessarily compact. We first establish the existence of an optimal ergodic occupation measure using only a near-monotone…
Recent research in economic theory attempts to study optimal economic growth and spatial location of economic activity in a unified framework. So far, the key result of this literature - asymptotic convergence, even in the absence of…
In this paper we analyze a mass transportation problem in a bounded domain with the possibility to transport mass to/from the boundary, paying the transport cost, that is given by the Euclidean distance plus an extra cost depending on the…
We establish a variant of Monge--Kantorovich duality for a constrained optimal transport problem with a continuum of agents, a finite set of alternatives, and general linear constraints. As an application, we revisit the large-market model…
We investigate the Lotka-Volterra model for predator-prey competition with a finite carrying capacity that varies periodically in time, modeling seasonal variations in nutrients or food resources. In the absence of time variability, the…
Due to rapid expansion of urban areas in recent years, management of curbside parking has become increasingly important. To mitigate congestion, while meeting a city's diverse needs, performance-based pricing schemes have received a…
Energy storage has great potential in grid congestion relief. By making large-scale energy storage portable through trucking, its capability to address grid congestion can be greatly enhanced. This paper explores a business model of…
We study a classical model for the atom that considers the movement of $n$ charged particles of charge $-1$ (electrons) interacting with a fixed nucleus of charge $\mu >0$. We show that two global branches of spatial relative equilibria…
We describe a competetive equillibrium in a railway cargo transportation model. We reduce the problem of finding this equillibrium to the solution of to mutually dual convex optimization problems. According to L.V. Kantorvich we interpret…
Solving the road congestion problem is one of the most pressing issues in moderncities since it causes time wasting, pollution, higher industrial costs and huge roadmaintenance costs. Advances in ITS technologies and the advent of…
We study stable allocations in an exchange economy with indivisible goods. The problem is well-known to be challenging, and rich enough to encode fundamentally unstable economies, such as the roommate problem. Our approach stems from…
In the field of optimal transport, two prominent subfields face each other: (i) unregularized optimal transport, "\`a-la-Kantorovich", which leads to extremely sparse plans but with algorithms that scale poorly, and (ii)…