Related papers: A new heap game
We develop an octonionic representation of the payoff function for three player, two strategy, maximally entangled quantum games in order to obtain computationally friendly version of this function. This computational capability is then…
We consider infinite duration alternating move games. These games were previously studied by Roth, Balcan, Kalai and Mansour. They presented an FPTAS for computing an approximated equilibrium, and conjectured that there is a polynomial…
We present a new family of Nim games where the rules depend on a given `coloring' of the tokens, each token being either black or white. The rules are as in Nim with the restriction that a white token on top of each heap is not allowed. We…
Energy parity games are infinite two-player turn-based games played on weighted graphs. The objective of the game combines a (qualitative) parity condition with the (quantitative) requirement that the sum of the weights (i.e., the level of…
This paper considers a time-varying game with $N$ players. Every time slot, players observe their own random events and then take a control action. The events and control actions affect the individual utilities earned by each player. The…
In this paper, we propose a Quantum variation of combinatorial games, generalizing the Quantum Tic-Tac-Toe proposed by Allan Goff. A combinatorial game is a two-player game with no chance and no hidden information, such as Go or Chess. In…
We introduce a two-player game in which one and his/her opponent attempt to pack as many ``prisoners'' as possible on the squares of an n-by-n checkerboard; each prisoner has to be ``protected'' by at least as many guards as the number of…
We build new quantum games, similar to the spin flip game, where as a novelty the players perform measurements on a quantum system associated to a continuous time search algorithm. The measurements collapse the wave function into one of the…
We investigate a two player game called the $K^4$-building game: two players alternately claim edges of an infinite complete graph. Each player's aim is to claim all six edges on some vertex set of size four for themself. The first player…
We analyze the computational complexity of two 2-player games involving packing objects into a box. In the first game, players alternate drawing polycubes from a shared pile and placing them into an initially empty box in any available…
We give a bijection between permutations of length 2n and certain pairs of Dyck paths with labels on the down steps. The bijection arises from a game in which two players alternate selecting from a set of 2n items: the permutation encodes…
Zeckendorf proved that every positive integer $n$ can be written uniquely as the sum of non-adjacent Fibonacci numbers; a similar result, though with a different notion of a legal decomposition, holds for many other sequences. We use these…
We introduce a new combinatorial game, named Triangle Game. In this game, a directed $3$-cycle graph is given, and tokens are placed on each vertex. The player chooses an edge and takes at least one token from the initial vertex. At the…
Zeckendorf proved that every positive integer $n$ can be written uniquely as the sum of non-adjacent Fibonacci numbers; a similar result holds for other positive linear recurrence sequences. These legal decompositions can be used to…
The semigroup game is a two-person zero-sum game defined on a semigroup S as follows: Players 1 and 2 choose elements x and y in S, respectively, and player 1 receives a payoff f(xy) defined by a function f from S to [-1,1]. If the…
Zeckendorf proved that every natural number $n$ can be expressed uniquely as a sum of non-consecutive Fibonacci numbers, called its Zeckendorf decomposition. Baird-Smith, Epstein, Flint, and Miller created the Zeckendorf game, a two-player…
This paper describes a new algorithm for decision making in two-player real-time video games. As with Monte Carlo Tree Search, the algorithm can be used without heuristics and has been developed for use in general video game AI. The…
We define a variant of the two-dimensional Silver Dollar game. Two coins are placed on a chessboard of unbounded size, and two players take turns choosing one of the coins and moving it. Coins are to be moved to the left or upward…
We show that the winning positions of a certain type of two-player game form interesting patterns which often defy analysis, yet can be computed by a cellular automaton. The game, known as {\em Blocking Wythoff Nim}, consists of moving a…
Ultimate Tic-Tac-Toe is a variant of the well known tic-tac-toe (noughts and crosses) board game. Two players compete to win three aligned "fields", each of them being a tic-tac-toe game. Each move determines which field the next player…