Related papers: PRIMES STEP Plays Games
This short note is devoted to the unraveling of the hidden interactivity of ordinary games which is an artefact of predictions of the behaviour of other players by the fixed player and describes deviations of their real behaviour from such…
Adding game elements to higher education is an increasingly common practice. As a result, many recent empirical studies focus on studying the effectiveness of gamified or game-based educational experiences. The findings of these studies are…
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…
We introduce a topological combinatorial game called the Link Smoothing Game. The game is played on the shadow of a link diagram and legal moves consist of smoothing precrossings. One player's goal is to keep the diagram connected while the…
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…
Distributed decision-makers are modeled as players in a game with two levels. High level decisions concern the game environment and determine the willingness of the players to form a coalition (or group). Low level decisions involve the…
We introduce the category of optiongraphs and option-preserving maps as a model to study impartial combinatorial games. Outcomes, remoteness, and extended nim-values are preserved under option-preserving maps. We show that the four…
In 1973 Fraenkel discovered interesting sequences which split the positive integers. These sequences became famous, because of a related unsolved conjecture. Here we construct combinatorial games, with `playable' rulesets, with these…
This is an introduction into John Conway's beautiful Combinatorial Game Theory, providing precise statements and detailed proofs for the fundamental parts of his theory. (1) Combinatorial game theory, (2) the GROUP of games, (3) the FIELD…
Coordination games have been of interest to game theorists, economists, and ecologists for many years to study such problems as the emergence of local conventions and the evolution of cooperative behavior. Approaches for understanding the…
This thesis presents some geometric insights into three different types of two player prediction games -- namely general learning task, prediction with expert advice, and online convex optimization. These games differ in the nature of the…
We introduce a new class of games where each player's aim is to randomise her strategic choices in order to affect the other players' expectations aside from her own. The way each player intends to exert this influence is expressed through…
The game of nim, with its simple rules, its elegant solution and its historical importance is the quintessence of a combinatorial game, which is why it led to so many generalizations and modifications. We present a modification with a new…
We present evidence from three student interactions in which two types of common solution methods for solving simple first-order differential equations are used. We describe these using the language of resources, considering epistemic games…
A circular Nim game is a two player impartial combinatorial game consisting of n stacks of tokens placed in a circle. A move consists of choosing k consecutive stacks, and taking at least one token from one or more of the k stacks. The last…
We introduce the class of pay or play games, which captures scenarios in which each decision maker is faced with a choice between two actions: one with a fixed payoff and an- other with a payoff dependent on others' selected actions. This…
We introduce a new family of Parrondo's games of alternating losing strategies in order to get a winning result. In our version of the games we consider an ensemble of players and use "social" rules in which the probabilities of the games…
Engagement in educational games, a recently popular academic topic, has been shown to increase learning performance, as well as a number of attitudinal factors, such as intrinsic interest and motivation. However, there is a lack of research…
An important class of differential interactive games, namely, one of the laced interactive games is considered. A posteriori analysis of such games (including the virtual a posteriori decomposition of a collective control) is discussed.…
The domatic number of a graph is the maximum number of pairwise disjoint dominating sets admitted by the graph. We introduce a game based around this graph invariant. The domatic number game is played on a graph $G$ by two players, Alice…