Related papers: Positional Games
In 1973 Fraenkel discovered interesting sequences which split the positive integers. These sequences became famous, because of a related unsolved conjecture. Here we construct combinatorial games, with `playable' rulesets, with these…
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 paper models games where the strategies are nodes of a graph G (we denote them as G-games) and in presence of coalition structures. The cases of one-shot and repeated games are presented. In the latter situation, coalitions are assumed…
Combinatorial games are two-player games of pure strategy where the players, usually called Left and Right, move alternately. In this paper, we introduce Cheating Robot games. These arise from simultaneous-play combinatorial games where one…
We start with the well-known game below: Two players hold a sheet of paper to their forehead on which a positive integer is written. The numbers are consecutive and each player can only see the number of the other one. In each time step,…
A matching game is a cooperative profit game defined on an edge-weighted graph, where the players are the vertices and the profit of a coalition is the maximum weight of matchings in the subgraph induced by the coalition. A population…
We study natural strategic games on directed graphs, which capture the idea of coordination in the absence of globally common strategies. We show that these games do not need to have a pure Nash equilibrium and that the problem of…
The class of passable games was recently introduced by Selinger as a class of combinatorial games that are suitable for modelling monotone set coloring games such as Hex. In a monotone set coloring game, the players alternately color the…
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 paper introduces a hierarchical framework for population games, where individuals delegate decision-making to proxies that act within their own strategic interests. This framework extends classical population games, where individuals…
Combinatorial games are played under two different play conventions: normal play, where the last player to move wins, and \mis play, where the last player to move loses. Combinatorial games are also classified into impartial positions and…
This paper uses category theory to develop an entirely new approach to approximate game theory. Game theory is the study of how different agents within a multi-agent system take decisions. At its core, game theory asks what an optimal…
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…
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…
We introduce the class of pay or play games, which captures scenarios in which each decision maker is faced with a choice between two actions: one with a fixed payoff and an- other with a payoff dependent on others' selected actions. This…
Subtraction games are a class of impartial combinatorial games whose positions correspond to nonnegative integers and whose moves correspond to subtracting one of a fixed set of numbers from the current position. Though they are easy to…
Evolutionary game theory has been a successful tool to combine classical game theory with learning-dynamical descriptions in multiagent systems. Provided some symmetric structures of interacting players, many studies have been focused on…
Spatial evolutionary games model individuals who are distributed in a spatial domain and update their strategies upon playing a normal form game with their neighbors. We derive integro-differential equations as deterministic approximations…
We study hedonic coalition formation games in which cooperation among the players is restricted by a graph structure: a subset of players can form a coalition if and only if they are connected in the given graph. We investigate the…
Game theory is the mathematical framework for analyzing strategic interactions in conflict and competition situations. In recent years quantum game theory has earned the attention of physicists, and has emerged as a branch of quantum…