Related papers: PRIMES STEP Plays Games
We model a dynamic public good contribution game, where players are (naturally) formed into groups. The groups are exogenously placed in a sequence, with limited information available to players about their groups' position in the sequence.…
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 $G$…
The main challenge of combinatorial game theory is to handle combinatorial chaos, if one player knows the strategy better than his opponent, he is able to determine the exact results of a game. If both players are qualified competitor, the…
PRIMES STEP is a mathematical outreach program established at MIT in 2015. STEP students study advanced topics beyond the school curriculum and conduct group research projects, often leading to publication. This article discusses the…
When learning to play an imperfect information game, it is often easier to first start with the basic mechanics of the game rules. For example, one can play several example rounds with private cards revealed to all players to better…
A game theoretic distributed decision making approach is presented for the problem of control effort allocation in a robotic team based on a novel variant of fictitious play. The proposed learning process allows the robots to accomplish…
We encode arbitrary finite impartial combinatorial games in terms of lattice points in rational convex polyhedra. Encodings provided by these \emph{lattice games} can be made particularly efficient for octal games, which we generalize to…
We introduce the concept of a multi-principal assistance game (MPAG), and circumvent an obstacle in social choice theory, Gibbard's theorem, by using a sufficiently collegial preference inference mechanism. In an MPAG, a single agent…
In this article, we present our findings from ten years of research on intelligent educational games. We discuss the architecture of our training environments for learning spelling and mathematics, and specifically focus on the…
Subtraction games are a class of impartial combinatorial games whose positions correspond to nonnegative integers and whose moves correspond to subtracting one of a fixed set of numbers from the current position. Though they are easy to…
Gamification refers to the process of adding game elements to a task. Of late, this process has been introduced in pedagogical settings to capture the attention and interest of students. In our study, we apply the process to Anatomy…
A poset game is a two-player game played over a partially ordered set (poset) in which the players alternate choosing an element of the poset, removing it and all elements greater than it. The first player unable to select an element of the…
We introduce a new type of positional games, played on a vertex set of a graph. Given a graph $G$, two players claim vertices of $G$, where the outcome of the game is determined by the subgraphs of $G$ induced by the vertices claimed by…
This paper introduces a collection of board games specifically chosen to serve as a basis for programming exercises. We examine the attractiveness of board games in this context as well as features that make a particular game a good…
We study variations on combinatorial games in which, instead of alternating moves, the players bid with discrete bidding chips for the right to determine who moves next. We consider both symmetric and partisan games, and explore differences…
Manipulatives used in the right way help improve mathematical concepts leading to better learning outcomes. In this paper, we present a phygital (physical + digital) curriculum inspired teaching system for kids aged 5-8 to learn geometry…
We define a new impartial combinatorial game, Flag Coloring, based on flood filling. We then generalize to a graph game, and find values for many positions on two colors. We demonstrate that the generalized game is PSPACE-complete for two…
Simple stochastic games are turn-based 2.5-player zero-sum graph games with a reachability objective. The problem is to compute the winning probability as well as the optimal strategies of both players. In this paper, we compare the three…
In this paper, we introduce a two-player impartial game on graphs, called a {\em feedback game}, which is a variant of the generalized geography. We study the feedback game on Eulerian graphs. In particular, we show that the…
Mathematical reasoning with algebraic and graphical representations is essential for success in physics courses. Many problems require students to fluently move between algebraic and graphical representations. We developed a freely…