Related papers: PRIMES STEP Plays Games
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…
This paper introduces alignment games, a new class of zero-sum games modeling strategic interventions where effectiveness depends on alignment with an underlying hidden state. Motivated by operational problems in medical diagnostics,…
For normal play, impartial games, we define penults as those positions in which every option results in an immediate win for the other player. We explore the number of tokens in penults of two positional games, Impartial Tic and Impartial…
Combinatorial Game Theory typically studies sequential rulesets with perfect information where two players alternate moves. There are rulesets with {\em entailing moves} that break the alternating play axiom and/or restrict the other…
This entry introduces educational games in secondary schools. Educational games include three main types of educational activities with a playful learning intention supported by digital technologies: educational serious games, educational…
In this paper, we analyze the mis\`ere versions of two impartial combinatorial games: k-Bounded Greedy Nim and Greedy Nim. We present a complete solution to both games by showing necessary and sufficient conditions for a position to be…
We define two impartial games, the Relator Achievement Game $\texttt{REL}$ and the Relator Avoidance Game $\texttt{RAV}$. Given a finite group $G$ and generating set $S$, both games begin with the empty word. Two players form a word in $S$…
We analyze a two-player game in which players take turns avoiding the selection of certain points within a convex geometry. The objective is to prevent the convex closure of all chosen points from encompassing a predefined set. The first…
The preference graph is a combinatorial representation of the structure of a normal-form game. Its nodes are the strategy profiles, with an arc between profiles if they differ in the strategy of a single player, where the orientation…
This paper studies a large class of two-player perfect-information turn-based parity games on infinite graphs, namely those generated by collapsible pushdown automata. The main motivation for studying these games comes from the connections…
Mutual imitation games among artificial birds are studied. By employing a variety of mappings and game rules, the evolution to the edge between chaos and windows is universally confirmed. Some other general features are observed, including…
Negotiations, a model of concurrency with multi party negotiation as primitive, have been recently introduced by J. Desel and J. Esparza. We initiate the study of games for this model. We study coalition problems: can a given coalition of…
Autism spectrum disorder is a neurodevelopmental condition that includes issues with communication and social interactions. People with ASD also often have restricted interests and repetitive behaviors. In this paper we build preliminary…
Given two finite sets of integers $S\subseteq\NNN\setminus\{0\}$ and $D\subseteq\NNN\setminus\{0,1\}$,the impartial combinatorial game $\IMARK(S,D)$ is played on a heap of tokens. From a heap of $n$ tokens, each player can moveeither to a…
The Game of Poker Chips, Dominoes and Survival fosters team building and high level cooperation in large groups, and is a tool applied in management training exercises. Each player, initially given two colored poker chips, is allowed to…
The multiplication game is a two-person game in which each player chooses a positive integer without knowledge of the other player's number. The two numbers are then multiplied together and the first digit of the product determines the…
Getting a group to adopt cooperative norms is an enduring challenge. But in real-world settings, individuals don't just passively accept static environments, they act both within and upon the social systems that structure their…
In this expository article intended to be accessible to undergraduate students we introduce a finite abelian group that can be associated to any finite connected graph. This group can be defined in an elementary combinatorial way in terms…
We attempt to automate various artistic processes by inventing a set of drawing games, analogous to the approach taken by emergent language research in inventing communication games. A critical difference is that drawing games demand much…
Game theory has by now found numerous applications in various fields, including economics, industry, jurisprudence, and artificial intelligence, where each player only cares about its own interest in a noncooperative or cooperative manner,…