Related papers: Hex implies Y
We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…
We characterize Nash equilibrium by postulating coherent behavior across varying games. Nash equilibrium is the only solution concept that satisfies the following axioms: (i) strictly dominant actions are played with positive probability,…
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 $G$…
Starting with a graph, two players take turns in either deleting an edge or deleting a vertex and all incident edges. The player removing the last vertex wins. We review the known results for this game and extend the computation of…
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…
We define notions of cautiousness and cautious belief to provide epistemic conditions for iterated admissibility in finite games. We show that iterated admissibility characterizes the behavioral implications of "cautious rationality and…
We consider a game played on an initially empty graph where two players alternate drawing an edge between vertices subject to the condition that no degree can exceed $k$. We show that for $k=3$, either player can avoid a Hamilton cycle, and…
We construct a sequence of finite graphs that weakly converge to a Cayley graph, but there is no labelling of the edges that would converge to the corresponding Cayley diagram. A similar construction is used to give graph sequences that…
Risk is a well-known turn based board game where the primary objective is nothing less than the world domination. Gameplay is based on battles between armies located in adjacent territories on the map of Earth. The combat's outcome is…
We show that any cooperative game can be represented by an assignment of costly facilities to players, in which it is intuitively obvious how to allocate the total cost in an equitable manner. This equitable solution turns out to be the…
Hedonic games provide a natural model of coalition formation among self-interested agents. The associated problem of finding stable outcomes in such games has been extensively studied. In this paper, we identify simple conditions on…
We give a simple short proof of Brooks' theorem using only induction and greedy coloring, while avoiding issues of graph connectivity. The argument generalizes easily to some extensions of Brooks' theorem, including its variants for list…
We adapt the method used by Jaynes to derive the equilibria of statistical physics to instead derive equilibria of bounded rational game theory. We analyze the dependence of these equilibria on the parameters of the underlying game,…
The mu-calculus is a powerful tool for specifying and verifying transition systems, including those with both demonic and angelic choice; its quantitative generalisation qMu extends that to probabilistic choice. We show that for a…
We explain a highly efficient algorithm for playing the simplest type of dots and boxes endgame optimally (by which we mean "in such a way so as to maximise the number of boxes that you take"). The algorithm is sufficiently simple that it…
An axiomatisation of Hurkens's paradox in dependent type theory is given without assuming any impredicative feature of said type theory.
We study a game where two players take turns selecting points of a convex geometry until the convex closure of the jointly selected points contains all the points of a given winning set. The winner of the game is the last player able to…
Game semantics and winning strategies offer a potential conceptual bridge between semantics and proof systems of logics. We illustrate this link for hybrid logic -- an extension of modal logic that allows for explicit reference to worlds…
The main purpose of the paper is the proof of a cardinal inequality for a space with points $G_\delta$, obtained with the help of a long version of the Menger game. This result improves a similar one of Scheepers and Tall.
This paper introduced a pursuit and evasion game to be played on a connected graph. One player moves invisibly around the graph, and the other player must guess his position. At each time step the second player guesses a vertex, winning if…