Related papers: Lights Out on graphs
The transmission switching problem aims to determine the optimal network topology that minimizes the operating costs of a power system. This problem is typically formulated as a mixed-integer optimization model, which involves big-M…
The present paper deals with connected subtraction games in graphs, which are generalization of takeaway games. In a connected subtraction game, two players alternate removing a connected sub-graph from a given connected game-graph,…
After the social learning models were proposed, finding the solutions of the games becomes a well-defined mathematical question. However, almost all papers on the games and their applications are based on solutions built upon either an…
We study stochastic evolution of optional games on simple graphs. There are two strategies, A and B, whose interaction is described by a general payoff matrix. In addition there are one or several possibilities to opt out from the game by…
We present new combinatorial objects, which we call grid-labelled graphs, and show how these can be used to represent the quantum states arising in a scenario which we refer to as the faulty emitter scenario: we have a machine designed to…
In this paper, we study a theoretical math problem of game theory and calculus of variations in which we minimize a functional involving two players. A general relationship between the optimal strategies for both players is presented,…
Systems of fixpoint equations over complete lattices, consisting of (mixed) least and greatest fixpoint equations, allow one to express a number of verification tasks such as model-checking of various kinds of specification logics or the…
This article deals with input-to-state stability (ISS) of discrete-time switched systems. Given a family of nonlinear systems with exogenous inputs, we present a class of switching signals under which the resulting switched system is ISS.…
Motivated by the success of domination games and by a variation of the coloring game called the indicated coloring game, we introduce a version of domination games called the indicated domination game. It is played on an arbitrary graph $G$…
We study vertex colourings of digraphs so that no out-neighbourhood is monochromatic and call such a colouring an {\bf out-colouring}. The problem of deciding whether a given digraph has an out-colouring with only two colours (called a…
We consider the following two-player game on a graph. A token is located at a vertex, and the players take turns to move it along an edge to a vertex that has not been visited before. A player who cannot move loses. We analyze outcomes with…
We study the problem of arithmetic billiards from a new perspective. We first raise a similar problem about reflecting lights inside grids. For the solution to this problem, we will give three proofs. Next, we consider a similar problem in…
The slow-coloring game is played by Lister and Painter on a graph $G$. On each round, Lister marks a nonempty subset $M$ of the uncolored vertices, scoring $|M|$ points. Painter then gives a color to a subset of $M$ that is independent in…
We formulate a class of mean field games on a finite state space with variational principles resembling those in continuous-state mean field games. We construct a controlled continuity equation featuring a nonlinear activation function on…
The \emph{slow-coloring game} is played by Lister and Painter on a graph $G$. Initially, all vertices of $G$ are uncolored. In each round, Lister marks a nonempty set $M$ of uncolored vertices, and Painter colors a subset of $M$ that is…
Stochastic games combine controllable and adversarial non-determinism with stochastic behavior and are a common tool in control, verification and synthesis of reactive systems facing uncertainty. Multi-objective stochastic games are natural…
Recently the matcher game was introduced. In this game, two players create a maximal matching by one player repeatedly choosing a vertex and the other player choosing a $K_2$ containing that vertex. One player tries to minimize the result…
In this work we address a game theoretic variant of the shortest path problem, in which two decision makers (players) move together along the edges of a graph from a given starting vertex to a given destination. The two players take turns…
Several problems in planning and reactive synthesis can be reduced to the analysis of two-player quantitative graph games. {\em Optimization} is one form of analysis. We argue that in many cases it may be better to replace the optimization…
A simple but nontrivial class of the quantum strategies in buying-selling games is presented. The player moves are a rational buying and an unconditional selling. The possibility of gaining extremal profits in such the games is considered.…