Related papers: The Nash problem for torus actions of complexity o…
We show that there exists a strong connection between the generic formal neighborhood at a rational arc lying in the Nash set associated with a toric divisorial valuation on a toric variety and the formal neighborhood at the generic point…
We systematically produce algebraic varieties with torus action by constructing them as suitably embedded subvarieties of toric varieties. The resulting varieties admit an explicit treatment in terms of toric geometry and graded ring…
This paper deals with the Nash problem, which consists in proving that the number of families of arcs on a singular germ of a surface $S$ coincides with the number of irreducible components of the exceptional divisor in the minimal…
Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet…
This paper studies the axiomatic bargaining problem and proposes a new class of bargaining solutions, called coarse Nash solutions. These solutions assign to each problem a set of outcomes coarser than that chosen by the classical Nash…
We study the problem of computing all Nash equilibria of a subclass of finite normal form games. With algebraic characterization of the games, we present a method for computing all its Nash equilibria. Further, we present a method for…
The Nash problem on arcs for normal surface singularities states that there are as many arc families on a germ (S,O) of a singular surface as there are essential divisors over (S,O). It is known that this problem can be reduced to the study…
We give an explicit description of the divisor class groups of rational trinomial varieties. As an application, we relate the iteration of Cox rings of any rational variety with torus action of complexity one to that of a Du Val surface.
We study the computational complexity of Nash equilibria in concurrent games with limit-average objectives. In particular, we prove that the existence of a Nash equilibrium in randomised strategies is undecidable, while the existence of a…
Let X be a normal affine T-variety of complexity at most one over a perfect field k, where T stands for the split algebraic torus. Our main result is a classification of additive group actions on X that are normalized by the T-action. This…
Nash equilibrium serves as a fundamental mathematical tool in economics and game theory. However, it classically assumes knowledge of player utilities, whereas economics generally regards preferences as more fundamental. To leverage…
We address Nash problem for surface singularities using wedges. We give a refinement of the characterisation of A. Reguera of the image of the Nash map in terms of wedges. Our improvement consists in a characterisation of the bijectivity of…
The Nash problem asks about the existence of a correspondence between families of arcs through singularities of complex varieties and certain types of divisorial valuations. It has been positively settled in dimension 2 by Fern\'andez de…
The Nash equilibrium problem is a widely used tool to model non-cooperative games. Many solution methods have been proposed in the literature to compute solutions of Nash equilibrium problems with continuous strategy sets, but, besides some…
This paper is intended to give a characterization of the optimality case in Nash's inequality, based on methods of nonlinear analysis for elliptic equations and techniques of the calculus of variations. By embedding the problem into a…
We give an affirmative answer to Nash Problem for quotient surface singularities, in particular for the icosahedral singularity $E_8$.
Economists were content with the concept of the Nash equilibrium as game theory's solution concept until Daskalakis, Goldberg, and Papadimitriou showed that finding a Nash equilibrium is most likely a computationally hard problem, a result…
We propose a method to compute a desingularization of a normal affine variety X endowed with a torus action in terms of a combinatorial description of such a variety due to Altmann and Hausen. This desingularization allows us to study the…
We characterize Nash equilibrium by postulating coherent behavior across varying games. Nash equilibrium is the only solution concept that satisfies the following axioms: (i) strictly dominant actions are played with positive probability,…
A new proof of equivariant resolution of singularities under a finite group action in characteristic 0 is provided. We assume we know how to resolve singularities without group action. We first prove equivariant resolution of toroidal…