相关论文: Games on the Sperner Triangle

We study two-player inclusion games played over word-generating higher-order recursion schemes. While inclusion checks are known to capture verification problems, two-player games generalize this relationship to program synthesis. In such…

We study multi-player turn-based games played on (potentially infinite) directed graphs. An outcome is assigned to every play of the game. Each player has a preference relation on the set of outcomes which allows him to compare plays. We…

We expand the theory of pebbling to graphs with weighted edges. In a weighted pebbling game, one player distributes a set amount of weight on the edges of a graph and his opponent chooses a target vertex and places a configuration of…

Despite its long history, the classical game of peg solitaire continues to attract the attention of the scientific community. In this paper, we consider two problems with an algorithmic flavour which are related with this game, namely…

Subset take-away is a two-player game involving a fixed finite set A. Players alternate choosing a proper, non-empty subset of A, with the condition that one may not name a set containing a set that was named earlier. A player unable to…

Kakutani's fixed point theorem is a generalization of Brouwer's fixed point theorem to upper semicontinuous multivalued maps and is used extensively in game theory and other areas of economics. Earlier works have shown that Sperner's lemma…

A combinatorial game is a two-player game without hidden information or chance elements. One of the major approaches to analyzing games in combinatorial game theory is to break down a given game position into a disjunctive sum of multiple…

We examine a two-person game we call Will-Testing in which the strategy space for both players is a real number. It has no equilibrium. When an infinitely large set of players plays this in all possible pairings, there is an equilibrium for…

We introduce and study pawn games, a class of two-player zero-sum turn-based graph games. A turn-based graph game proceeds by placing a token on an initial vertex, and whoever controls the vertex on which the token is located, chooses its…

Both the USA TST 2008 and the ELMO Shortlist 2013 suggested two issues that are connected to fixed points. These problems provide a strong linkage between the various attributes of specific points in a triangle. In this article, we will…

We introduce a three-player nonlocal game, with a finite number of classical questions and answers, such that the optimal success probability of $1$ in the game can only be achieved in the limit of strategies using arbitrarily…

We consider average-energy games, where the goal is to minimize the long-run average of the accumulated energy. While several results have been obtained on these games recently, decidability of average-energy games with a lower-bound…

This paper considers a class of two-player zero-sum games on directed graphs whose vertices are equipped with random payoffs of bounded support known by both players. Starting from a fixed vertex, players take turns to move a token along…

We propose a learning dynamics to model how strategic agents repeatedly play a continuous game while relying on an information platform to learn an unknown payoff-relevant parameter. In each time step, the platform updates a belief estimate…

Quantum game theory is a recently developing field of physical research. In this paper, we investigate quantum games in a systematic way. With the famous instance of the Prisoner's Dilemma, we present the fascinating properties of quantum…

The main goal of the paper is the full 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, which improves a similar one of Scheepers and Tall, was…

We consider the following two-player game on a graph. A token is located at a vertex, and the players take turns to move it along an edge to a vertex that has not been visited before. A player who cannot move loses. We analyze outcomes with…

This paper presents a case study for the application of semiring semantics for fixed-point formulae to the analysis of strategies in B\"uchi games. Semiring semantics generalizes the classical Boolean semantics by permitting multiple truth…

We show how solutions to many recursive arena equations can be computed in a natural way by allowing loops in arenas. We then equip arenas with winning functions and total winning strategies. We present two natural winning conditions…

Given a fixed graph $H$ and a positive integer $n$, a Picker-Chooser $H$-game is a biased game played on the edge set of $K_n$ in which Picker is trying to force many copies of $H$ and Chooser is trying to prevent him from doing so. In this…