Related papers: Exploring Tetris as a Transformation Semigroup
Evolutionary game theory is a powerful framework for studying evolution in populations of interacting individuals. A common assumption in evolutionary game theory is that interactions are symmetric, which means that the players are…
We define and study a collection of matroid isomorphism games corresponding to various axiomatic characterizations of matroids. These are nonlocal games played between two cooperative players. Each game is played on two matroids, and the…
The main goal of this paper is to settle a conceptual framework for cooperative game theory in which the notion of composition/aggregation of games is the defining structure. This is done via the mathematical theory of algebraic operads: we…
We study zero-sum games, a variant of the classical combinatorial Subtraction games (studied for example in the monumental work "Winning Ways", by Berlekamp, Conway and Guy), called Cumulative Subtraction (CS). Two players alternate in…
We introduce the concept of an extension of a semilattice of groups $A$ by a group $G$ and describe all the extensions of this type which are equivalent to the crossed products $A*_\Theta G$ by twisted partial actions $\Theta$ of $G$ on…
In evolutionary game theory, repeated two-player games are used to study strategy evolution in a population under natural selection. As the evolution greatly depends on the interaction structure, there has been growing interests in studying…
We are investigating who has the winning strategy in a game in which two players take turns drawing arrows trying to complete cycle cells in a graph. A cycle cell is a cycle with no chords. We examine game boards where the winning strategy…
In this Letter we present a new perspective for the study of the Public Goods games on complex networks. The idea of our approach is to consider a realistic structure for the groups in which Public goods games are played. Instead of…
Muller games are played by two players moving a token along a graph; the winner is determined by the set of vertices that occur infinitely often. The central algorithmic problem is to compute the winning regions for the players. Different…
In this paper, we consider a class of $n$-person noncooperative games, where the utility function of every player is given by a homogeneous polynomial defined by the payoff tensor of that player, which is a natural extension of the bimatrix…
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…
We consider the permutation analogue of Penney's game for words. Two players, in order, each choose a permutation of length $k\ge3$; then a sequence of independent random values from a continuous distribution is generated, until the…
Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…
We classify an algebraic phenomenon on certain families of wreath products that can be seen as coming from a family of puzzles about switches on the corners of a spinning table. Such puzzles have been written about and generalized since…
We prove that the problem of reconstructing a permutation $\pi_1,\dotsc,\pi_n$ of the integers $[1\dotso n]$ given the absolute differences $|\pi_{i+1}-\pi_i|$, $i = 1,\dotsc,n-1$ is NP-complete. As an intermediate step we first prove the…
A set of integers greater than 1 is primitive if no element divides another. Erd\H{o}s proved in 1935 that the sum of $1/(n \log n)$ for $n$ running over a primitive set $A$ is universally bounded over all choices for $A$. In 1988 he asked…
We consider the two-player game chomp on posets associated to numerical semigroups and show that the analysis of strategies for chomp is strongly related to classical properties of semigroups. We characterize, which player has a…
A permutation group is {\it binary} if its orbits on $k$-tuples, for any integer $k\geq 2$, can be deduced from its orbits on $2$-tuples. Cherlin conjectured that a finite primitive binary permutation group $G$ must lie in one of three…
We investigate a semigroup construction related to the two-sided wreath product. It encompasses a range of known constructions and gives a slightly finer version of the decomposition in the Krohn-Rhodes Theorem, in which the three-element…
A non-zero-sum 3-person coalition game is presented, to study the evolution of complexity and diversity in cooperation, where the population dynamics of players with strategies is given according to their scores in the iterated game and…