Related papers: Playing Games with Cacti
This paper focuses on a kind of linear quadratic non-zero sum differential game driven by backward stochastic differential equation with asymmetric information, which is a natural continuation of Wang and Yu [IEEE TAC (2010) 55: 1742-1747,…
Circular Nim is a two-player impartial combinatorial game consisting of $n$ stacks of tokens placed in a circle. A move consists of choosing $k$ consecutive stacks and taking at least one token from one or more of the stacks. The last…
Graph games of infinite length are a natural model for open reactive processes: one player represents the controller, trying to ensure a given specification, and the other represents a hostile environment. The evolution of the system…
We study the Maker-Maker version of the domination game introduced in 2018 by Duch\^ene et al. Given a graph, two players alternately claim vertices. The first player to claim a dominating set of the graph wins. As the Maker-Breaker…
We study a discrete diffusion process introduced in some combinatorial games called FLOODIT and MADVIRUS that can be played online and whose computational complexity has been recently studied by Arthur et al (FUN'2010). The flooding…
Fictitious play (FP) is a natural learning dynamic in two-player zero-sum games. Samuel Karlin conjectured in 1959 that FP converges at a rate of $O(t^{-1/2})$ to Nash equilibrium, where $t$ is the number of steps played. However,…
In this paper I give a brief introduction to a family of simple but non-trivial models designed to increase our understanding of collective processes in markets, the so-called Minority Games, and their non-equilibrium statistical…
We investigate a two player game called the $K^4$-building game: two players alternately claim edges of an infinite complete graph. Each player's aim is to claim all six edges on some vertex set of size four for themself. The first player…
Parity games are infinite two-player games played on directed graphs. Parity game solvers are used in the domain of formal verification. This paper defines parametrized parity games and introduces an operation, Justify, that determines a…
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…
This work contains the mathematical exploration of a few prototypical games in which central concepts from statistics and probability theory naturally emerge. The first two kinds of games are termed Fisher and Bayesian games, which are…
Simple stochastic games are turn-based 2.5-player zero-sum graph games with a reachability objective. The problem is to compute the winning probability as well as the optimal strategies of both players. In this paper, we compare the three…
A configuration of the lit-only $\sigma$-game on a finite graph $\Gamma$ is an assignment of one of two states, on or off, to all vertices of $\Gamma.$ Given a configuration, a move of the lit-only $\sigma$-game on $\Gamma$ allows the…
This paper investigates the geometrical properties of real world games (e.g. Tic-Tac-Toe, Go, StarCraft II). We hypothesise that their geometrical structure resemble a spinning top, with the upright axis representing transitive strength,…
Evolutionary game theory is a common framework to study the evolution of cooperation, where it is usually assumed that the same game is played in all interactions. Here, we investigate a model where the game that is played by two…
The class of Guaranteed Scoring Games (GS) are two-player combinatorial games with the property that Normal-play games (Conway et. al.) are ordered embedded into GS. They include, as subclasses, the scoring games considered by Milnor…
We present tropical games, a generalization of combinatorial min-max games based on tropical algebras. Our model breaks the traditional symmetry of rational zero-sum games where players have exactly opposed goals (min vs. max), is more…
In classical game theory, optimal strategies are determined for games with complete information; this requires knowledge of the opponent's goals. We analyze games when a player is mistaken about their opponents goals. For definitiveness, we…
We introduce the game of Cat Herding, where an omnipresent herder slowly cuts down a graph until an evasive cat player has nowhere to go. The number of cuts made is the score of a game, and we study the score under optimal play. In this…
We consider the following two-player game: Maxi and Mini start with the empty graph on $n$ vertices and take turns, always adding one additional edge to the graph such that the chromatic number is at most $k$, where $k \in \mathbb{N}$ is a…