Related papers: The Nash problem for torus actions of complexity o…
The paper provides a computation of the equivariant Chow group of a rational, complete, complexity one $T$-variety
We study equivariant unirationality of actions of finite groups on tori of small dimensions.
In this paper we study the existence and uniqueness of Nash equilibria (solution to competition-wise problems, with several controls trying to reach possibly different goals) associated to linear partial differential equations and show…
Let $X$ be a 3-dimensional affine variety with a faithful action of a 2-dimensional torus $T$. Then the space of first order infinitesimal deformations $T^1(X)$ is graded by the characters of $T$, and the zeroth graded component $T^1(X)_0$…
This paper studies Nash equilibrium problems that are given by polynomial functions. We formulate efficient polynomial optimization problems for computing Nash equilibria. The Lasserre type Moment-SOS relaxations are used to solve them.…
We study optimal transport-based distributionally robust optimization problems where a fictitious adversary, often envisioned as nature, can choose the distribution of the uncertain problem parameters by reshaping a prescribed reference…
We describe explicitly the normalization of affine varieties with an algebraic torus action of complexity one in terms of polyhedral divisors. We also provide a description of homogeneous integrally closed ideals of affine T-varieties of…
For a complex variety with a torus action we propose a new method of computing Chern-Schwartz-MacPherson classes. The method does not apply resolution of singularities. It is based on Localization Theorem in equivariant cohomology.
The Hirzebruch $td_y(X)$ class of a complex manifold X is a formal combination of Chern characters of the sheaves of differential forms multiplied by the Todd class. The related $\chi_y$-genus admits a generalization for singular complex…
We study Nash implementation by stochastic mechanisms, and provide a surprisingly simple full characterization, which is in sharp contrast to the classical, albeit complicated, full characterization in Moore and Repullo (1990).
We give a combinatorial classification of torus equivariant vector bundles on a (normal) projective T-variety of complexity-one. This extends the classification of equivariant line bundles on complexity-one T-varieties by Petersen-S\"uss on…
We show that the presentation of affine $\mathbb{T}$-varieties of complexity one in terms of polyhedral divisors holds over an arbitrary field. We also describe a class of multigraded algebras over Dedekind domains. We study how the algebra…
We study surplus division in network constrained bilateral matching markets with transferable utility. We introduce a new solution concept, the credible bargaining solution, which refines stability by requiring that, for each matched pair…
Using the language of T-varieties, we study torus invariant curves on a complete normal variety $X$ with an effective codimension-one torus action. In the same way that the $T$-invariant Weil divisors on $X$ are sums of "vertical" divisors…
The preferences of players in non-cooperative games represent their choice in the set of available options, which meet the completeness property if players are able to compare any pair of available options. In the existing literature, the…
Nash`s classical bargaining solution suggests that n players in a non-cooperative bargaining situation should find a solution that maximizes the product of each player's utility functions. We consider a special case: Suppose that the…
We investigate a modular convex Nash equilibrium problem involving nonsmooth functions acting on linear mixtures of strategies, as well as smooth coupling functions. An asynchronous block-iterative decomposition method is proposed to solve…
We characterize all varieties with a torus action of complexity one that admit iteration of Cox rings.
Characterizations of Nash equilibrium, correlated equilibrium, and rationalizability in terms of common knowledge of rationality are well known. Analogous characterizations of sequential equilibrium, (trembling hand) perfect equilibrium,…
In this paper we present new proofs using real spectra of the finiteness theorem on Nash trivial simultaneous resolution and the finiteness theorem on Blow-Nash triviality for isolated real algebraic singularities. That is, we prove that a…