Related papers: Constructive comparison in bidding combinatorial g…
We examine short combinatorial games for three or more players under a new play convention in which a player who cannot move on their turn is the unique loser. We show that many theorems of impartial and partizan two-player games under…
Absolute combinatorial game theory was recently developed as a unifying tool for constructive/local game comparison (Larsson et al. 2018). The theory concerns {\em parental universes} of combinatorial games; standard closure properties are…
This article introduces differential hybrid games, which combine differential games with hybrid games. In both kinds of games, two players interact with continuous dynamics. The difference is that hybrid games also provide all the features…
We present and study a variant of the mean payoff games introduced by A. Ehrenfeucht and J. Mycielski. In this version, the second player makes an infinite sequence of moves only after the first player's sequence of moves has been decided…
The class of Guaranteed Scoring Games (GS) are two-player combinatorial games with the property that Normal-play games (Conway et. al.) are ordered embedded into GS. They include, as subclasses, the scoring games considered by Milnor…
We consider a single buyer with a combinatorial preference that would like to purchase related products and services from different vendors, where each vendor supplies exactly one product. We study the general case where subsets of products…
We study generalized games defined over Banach spaces using variational analysis. To reformulate generalized games as quasi-variational inequality problems, we will first form a suitable principal operator and study some significant…
The preferences of players in non-cooperative games represent their choice in the set of available options, which meet the completeness property if players are able to compare any pair of available options. In the existing literature, the…
In game theory, players have continuous expected payoff functions and can use fixed point theorems to locate equilibria. This optimization method requires that players adopt a particular type of probability measure space. Here, we introduce…
This thesis will be discussing scoring play combinatorial games and looking at the general structure of these games under different operators. I will also be looking at the Sprague-Grundy values for scoring play impartial games, and…
We survey recent developments in the theory of impartial combinatorial games in misere play, focusing on how the Sprague-Grundy theory of normal-play impartial games generalizes to misere play via the indistinguishability quotient…
Repeated games have a long tradition in the behavioral sciences and evolutionary biology. Recently, strategies were discovered that permit an unprecedented level of control over repeated interactions by enabling a player to unilaterally…
A combinatorial game is a two-player game without hidden information or chance elements. The disjunctive sum $G + H$ of games $G$ and $H$ is the game in which $G$ and $H$ are played in parallel, and a player makes a move on exactly one of…
Following the work of Lloyd Shapley on the Shapley value, and tangentially the work of Guillermo Owen, we offer an alternative non-probabilistic formulation of part of the work of Robert J. Weber in his 1978 paper "Probabilistic values for…
The assignment game, introduced by Shapley and Shubik (1971), is a classic model for two-sided matching markets between buyers and sellers. In the original assignment game, it is assumed that payments lead to transferable utility and that…
The performance of two pivoting algorithms, due to Lemke and Cottle and Dantzig, is studied on linear complementarity problems (LCPs) that arise from infinite games, such as parity, average-reward, and discounted games. The algorithms have…
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…
The paper reviews some axioms of additivity concerning ranking methods used for generalized tournaments with possible missing values and multiple comparisons. It is shown that one of the most natural properties, called consistency, has…
We develop a generic computational model that can be used effectively for establishing the existence of winning strategies for concrete finite combinatorial games. Our modelling is (equational) logic-based involving advanced techniques from…
We present a new model of incomplete information games without private information in which the players use a distributionally robust optimization approach to cope with the payoff uncertainty. With some specific restrictions, we show that…