Related papers: The Cardinality of Infinite Games

Repeated quantum game theory addresses long term relations among players who choose quantum strategies. In the conventional quantum game theory, single round quantum games or at most finitely repeated games have been widely studied, however…

Iterated admissibility is a well-known and important concept in classical game theory, e.g. to determine rational behaviors in multi-player matrix games. As recently shown by Berwanger, this concept can be soundly extended to infinite games…

We propose an interpretation of the infinite sum of combinatorial games. In such an interpretation, plays involve infinite runs, but without loops. The notion of a run is quite natural, but different possibilities arises for the notion of…

We study two-player games of infinite duration that are played on finite or infinite game graphs. A winning strategy for such a game is positional if it only depends on the current position, and not on the history of the play. A game is…

A framework for discussing relationships between different types of games is proposed. Within the framework, quantum simultaneous games, finite quantum simultaneous games, quantum sequential games, and finite quantum sequential games are…

This paper studies sequential quantum games under the assumption that the moves of the players are drawn from groups and not just plain sets. The extra group structure makes possible to easily derive some very general results characterizing…

We study multi-player games with perfect information and general payoff function, where the set of stages is the set of non-positive integers $\{\ldots,-2,-1,0\}$. We define two related equilibrium concepts: one considering only deviations…

Sequential equilibrium is one of the most fundamental refinements of Nash equilibrium for games in extensive form. However, it is not defined for extensive-form games in which a player can choose among a continuum of actions. We define a…

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…

This paper investigates some necessary and sufficient conditions for a game to be a potential game. At first, we extend the classical results of Slade and Monderer and Shapley from games with one-dimensional action spaces to games with…

For a topological space $X$ and a point $x \in X$, consider the following game -- related to the property of $X$ being countably tight at $x$. In each inning $n\in\omega$, the first player chooses a set $A_n$ that clusters at $x$, and then…

Combinatorial Game Theory is a branch of mathematics and theoretical computer science that studies sequential 2-player games with perfect information. Normal play is the convention where a player who cannot move loses. Here, we generalize…

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…

Given entropy's central role in multiple areas of physics and science, one important task is to develop a systematic and unifying approach to defining entropy. Games of chance become a natural candidate for characterising the uncertainty of…

We study 2-player turn-based perfect-information stochastic games with countably infinite state space. The players aim at maximizing/minimizing the probability of a given event (i.e., measurable set of infinite plays), such as reachability,…

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…

Combinatorial Game Theory has also been called `additive game theory', whenever the analysis involves sums of independent game components. Such {\em disjunctive sums} invoke comparison between games, which allows abstract values to be…

In this paper we investigate a differential game in which countably many dynamical objects pursue a single one. All the players perform simple motions. The duration of the game is fixed. The controls of a group of pursuers are subject to…

Game theory is the standard tool used to model strategic interactions in evolutionary biology and social science. Traditional game theory studies the equilibria of simple games. But is traditional game theory applicable if the game is…

Taking the absolute value of consecutive differences of a cyclicly ordered list of integers constitutes a simple dynamical system. For lists of lenght a power of two the process will terminate in all zeros, but examples with arbitarily long…