Related papers: Computational and Algebraic Structure of Board Gam…
Magic: the Gathering is a popular and famously complicated card game about magical combat. Recently, several authors including Chatterjee and Ibsen-Jensen (2016) and Churchill, Biderman, and Herrick (2019) have investigated the…
We propose a class of two person perfect information games based on weighted graphs. One of these games can be described in terms of a round pizza which is cut radially into pieces of varying size. The two players alternately take pieces…
We introduce quantum XOR games, a model of two-player one-round games that extends the model of XOR games by allowing the referee's questions to the players to be quantum states. We give examples showing that quantum XOR games exhibit a…
We study strategic games on weighted directed graphs, in which the payoff of a player is defined as the sum of the weights on the edges from players who chose the same strategy, augmented by a fixed non-negative integer bonus for picking a…
We apply a Bayesian agent-based framework inspired by QBism to iterations of two quantum games, the CHSH game and the quantum prisoners' dilemma. In each two-player game, players hold beliefs about an amount of shared entanglement and about…
We close the gap in the proof (published by Chen and Lin) of formulas for the minimum number of questions required in the expected case for Mastermind and its variant called AB game, where both games are played with two pegs and $n$ colors.…
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…
Combinatorial Game Theory has also been called `additive game theory', whenever the analysis involves sums of independent game components. Such {\em disjunctive sums} invoke comparison between games, which allows abstract values to be…
Conway Checkers is a game played with a checker placed in each square of the lower half of an infinite checkerboard. Pieces move by jumping over an adjacent checker, removing the checker jumped over. Conway showed that it is not possible to…
The Stackelberg equilibrium solution concept describes optimal strategies to commit to: Player 1 (termed the leader) publicly commits to a strategy and Player 2 (termed the follower) plays a best response to this strategy (ties are broken…
Circulant matrices are an important tool widely used in coding theory and cryptography. A circulant matrix is a square matrix whose rows are the cyclic shifts of the first row. Such a matrix can be efficiently stored in memory because it is…
A common format for sports contests involves pairwise matches between two teams, with the #1 player of team A matched against the #1 player of team B, the #2 player of team A against the #2 player of team B, and so on. This paper addresses…
A decision tree looks like a simple directed acyclic computational graph, where only the leaf nodes specify the output values and the non-terminals specify their tests or split conditions. From the numerical perspective, we express decision…
We show that the lattice games of Guo and Miller support universal computation, disproving their conjecture that all lattice games have rational strategies. We also state an explicit counterexample to that conjecture: a three dimensional…
We consider the dynamics of player's strategies in repeated market games, where the selection of strategies is determined by a learning model. Prior theoretical analysis and experimental data show that after large number of plays the…
We develop a new approach that computes approximate equilibrium strategies in Jotto, a popular word game. Jotto is an extremely large two-player game of imperfect information; its game tree has many orders of magnitude more states than…
Examples of games between two partners with mixed strategies, calculated by the use of the probability amplitude as some vector in Hilbert space are given. The games are macroscopic, no microscopic quantum agent is supposed. The reason for…
With the growth of the internet it is becoming increasingly important to understand how the behaviour of players is affected by the topology of the network interconnecting them. Many models which involve networks of interacting players have…
In the article a turn-based game played on four computers connected via network is investigated. There are three computers with natural intelligence and one with artificial intelligence. Game table is seen by each player's own view point in…
Quantum phenomena have remained largely inaccessible to the general public. This can be attributed to the fact that we do not experience quantum mechanics on a tangible level in our daily lives. Games can provide an environment in which…