Related papers: Impartial Games with Activeness
In 1901, Bouton proved that a winning strategy of the game of Nim is given by the bitwise XOR, called the nim-sum. But, why does such a weird binary operation work? Led by this question, this paper introduces a categorical reinterpretation…
Domineering is a combinatorial game played on a subset of a rectangular grid between two players. Each board position can be put into one of four outcome classes based on who the winner will be if both players play optimally. In this note,…
Inverse game theory is utilized to infer the cost functions of all players based on game outcomes. However, existing inverse game theory methods do not consider the learner as an active participant in the game, which could significantly…
Game theory provides a mathematical framework for analysing strategic situations involving at least two players. Normal-form games model situations where the players simultaneously pick their moves. In this thesis we explore the strategic…
Graph Pebbling is a well-studied single-player game on graphs. We introduce the game of Blocking Pebbles which adapts Graph Pebbling into a two-player strategy game in order to examine it within the context of Combinatorial Game Theory.…
As Aumann stated, cooperation and non-cooperation are different ways of viewing the same game, with the main difference being whether players can reach a binding cooperative agreement. In the real world, many games often coexist competition…
This paper addresses several significant gaps in the theory of restricted mis\`ere play (Plambeck, Siegel 2008), primarily in the well-studied universe of dead-ending games, $\mathcal{E}$ (Milley, Renault 2013); if a player run out of moves…
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…
We study a game for recognising formal languages, in which two players with imperfect information need to coordinate on a common decision, given private input words correlated by a finite graph. The players have a joint objective to avoid…
We introduce and study coverage games - a novel framework for multi-agent planning in settings in which a system operates several agents but does not have full control on them, or interacts with an environment that consists of several…
We study the conditions under which the iterated elimination of strictly dominated strategies is order independent and we identify a class of discontinuous games for which order does not matter. In this way, we answer the open problem…
Domineering is a two player game played on a checkerboard in which one player places dominoes vertically and the other places them horizontally. We give bivariate generating polynomials enumerating Domineering positions by the number of…
We consider a sub-class of bi-matrix games which we refer to as two-person (hereafter referred to as two-player) additively-separable sum (TPASS) games, where the sum of the pay-offs of the two players is additively separable. The row…
Candogan et al. (2011) provide an orthogonal direct-sum decomposition of finite games into potential, harmonic and nonstrategic components. In this paper we study the issue of decomposing games that are strategically equivalent from a…
Probabilistic game structures combine both nondeterminism and stochasticity, where players repeatedly take actions simultaneously to move to the next state of the concurrent game. Probabilistic alternating simulation is an important tool to…
In normal version of combinatorial game theory, all games are invertible, whereas only the empty game is invertible in mis\`ere version. For this reason, several restricted universes were earlier considered for their study, in which more…
Cooperative interval games are a generalized model of cooperative games in which the worth of every coalition corresponds to a closed interval representing the possible outcomes of its cooperation. Selections are all possible outcomes of…
Two-player quantitative zero-sum games provide a natural framework to synthesize controllers with performance guarantees for reactive systems within an uncontrollable environment. Classical settings include mean-payoff games, where the…
We study games with finitely many participants, each having finitely many choices. We consider the following categories of participants: (I) populations: sets of nonatomic agents, (II) atomic splittable players, (III) atomic non splittable…
We introduce and study Minkowski games. These are two player games, where the players take turns to chose positions in $\mathbb{R}^d$ based on some rules. Variants include boundedness games, where one player wants to keep the positions…