Related papers: Exploring Tetris as a Transformation Semigroup

Situations of conflict giving rise to social dilemmas are widespread in society and game theory is one major way in which they can be investigated. Starting from the observation that individuals in society interact through networks of…

We define a two-player combinatorial game in which players take alternate turns; each turn consists on deleting a vertex of a graph, together with all the edges containing such vertex. If any vertex became isolated by a player's move then…

Arc-Kayles is a game where two players alternate removing two adjacent vertices until no move is left, the winner being the player who played the last move. Introduced in 1978, its computational complexity is still open. More recently,…

Many recent practical and theoretical breakthroughs focus on adversarial team multi-player games (ATMGs) in ex ante correlation scenarios. In this setting, team members are allowed to coordinate their strategies only before the game starts.…

The relationship between topology and dynamics of complex systems has motivated continuing interest from the scientific community. In the present work, we address this interesting topic from the perspective of simple games, involving two…

In 1901, Bouton proved that a winning strategy of the game of Nim is given by the bitwise XOR, called the nim-sum. But, why does such a weird binary operation work? Led by this question, this paper introduces a categorical reinterpretation…

We study a class of algebras we regard as generalized Rock-Paper-Scissors games. We determine when such algebras can exist, show that these algebras generate the varieties generated by hypertournament algebras, count these algebras, study…

Simulating bipartite games, such as the trust game, is not straightforward due to the lack of a natural way to distinguish roles in a single population. The square lattice topology can provide a simple yet elegant solution by alternating…

We study the problem of computing an $\epsilon$-Nash equilibrium in repeated games. Earlier work by Borgs et al. [2010] suggests that this problem is intractable. We show that if we make a slight change to their model---modeling the players…

We introduce versions of game-theoretic semantics (GTS) for Alternating-Time Temporal Logic (ATL). In GTS, truth is defined in terms of existence of a winning strategy in a semantic evaluation game, and thus the game-theoretic perspective…

The peculiarity of adversarial team games resides in the asymmetric information available to the team members during the play, which makes the equilibrium computation problem hard even with zero-sum payoffs. The algorithms available in the…

In this paper we study the rotation and spatial inversion symmetry of regular tetrahedron. We obtain the representation matrix, multiplication table,the order of all group elements, all possible combinations of generator elements, the…

Recent work in deep reinforcement learning has allowed algorithms to learn complex tasks such as Atari 2600 games just from the reward provided by the game, but these algorithms presently require millions of training steps in order to…

We propose a new model of a distributed game, called an ATS game, which is played on a non-deterministic asynchronous transition system -- a natural distributed finite-state device working on Mazurkiewicz traces. This new…

Synchronous linear constraint system games are nonlocal games that verify whether or not two players share a solution to a given system of equations. Two algebraic objects associated to these games encode information about the existence of…

Semi-direct products of finite groups have permutation representations that are constructed from the permutation representations of their constituents. One can envision these in a metaphoric sense in which a rope is made from a bundle of…

In Combinatorial Game Theory, we study the set of games G, whose elements are mapped from positions of rulesets. In many case, given a ruleset, not all elements of G can be given as a position in the ruleset. It is an intriguing question…

Semigroup theory is a branch of abstract algebra, and it provides mathematical tools for the theory of computation. Finite semigroups can describe state transition systems and thus they model physically realizable computers. Engineering…

The game of SET is one of the best mathematical games ever. It is no wonder that people have tried to generalize it. We discuss existing generalizations of the game of SET to different groups. We concentrate on two types of generalization:…

In a game of permutation wordle, a player attempts to guess a secret permutation in the fewest number of guesses possible. Previously, Samuel Kutin and Lawren Smithline (arXiv:2408.00903) introduced this game and proposed a strategy called…