Related papers: A Simplified Game for Resolution of Singularities
Absolute Universes of combinatorial games, as defined in a recent paper by the same authors, include many standard short normal- mis\`ere- and scoring-play monoids. In this note we show that the class is categorical, by extending Joyal's…
The numbers game is a one-player game played on a finite simple graph with certain "amplitudes" assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at…
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.
Game Theory studies situations in which multiple agents having conflicting objectives have to reach a collective decision. The question of a compact representation language for agents utility function is of crucial importance since the…
In this paper, we address an instance of uniquely solvable mean-field game with a common noise whose corresponding counterpart without common noise has several equilibria. We study the selection problem for this mean-field game without…
We introduce a general systematic procedure for solving any binary-input binary-output game using operator algebraic techniques on the representation theory for the underlying group, which we then illustrate on the prominent class of tilted…
We fully characterize the core of a broad class of nonlinear games by identifying a suitable relaxation for inherent nonlinearity, directly generalizing the linear frameworks in the literature. This characterization significantly expands…
We discuss the problem of uniqueness of solutions for the Fubuki game when the diagonal is prescribed.
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…
We consider a randomized algorithm for the unique games problem, using independent multinomial probabilities to assign labels to the vertices of a graph. The expected value of the solution obtained by the algorithm is expressed as a…
In characteristic zero, we construct logarithmic resolution of singularities, with simple normal crossings exceptional divisor, using weighted blow-ups.
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
The Minority Game is a simple model for the collective behavior of agents in an idealized situation where they have to compete through adaptation for a finite resource. This review summarizes the statistical mechanics community efforts to…
The game of SET is a popular card game in which the objective is to form Sets using cards from a special deck. In this paper we study single- and multi-round variations of this game from the computational complexity point of view and…
This paper summarizes the results at the present moment about singularities with respect to the Mather-Jacobian log discrepancies over algebraically closed field of arbitrary characteristic. The basic point is the Inversion of Adjunction…
In this invited contribution, we propose a comprehensive introduction to game theory applied in computer aided synthesis. In this context, we give some classical results on two-player zero-sum games and then on multi-player non zero-sum…
The ``losing positions" of certain combinatorial games constitute linear error detecting and correcting codes. We show that a large class of games that can be cast in the form of *annihilation games*, provides a potentially polynomial…
The Nakamura number is an appropriate invariant of a simple game to study the existence of social equilibria and the possibility of cycles. For symmetric quota games its number can be obtained by an easy formula. For some subclasses of…
We consider the general model of zero-sum repeated games (or stochastic games with signals), and assume that one of the players is fully informed and controls the transitions of the state variable. We prove the existence of the uniform…
Our paper explores the game theoretic value of the 7-in-a-row game. We reduce the problem to solving a finite board game, which we target using Proof Number Search. We present a number of heuristic improvements to Proof Number Search and…