Related papers: Niel's Chess -- Rules for Xiangqi
Applying neural network (NN) methods in games can lead to various new and exciting game dynamics not previously possible. However, they also lead to new challenges such as the lack of large, clean datasets, varying player skill levels, and…
This paper aims to study the graph radii and diameters induced by the $k$-dimensional versions of the well-known six international chess pieces on every finite $\{n \times n \times \dots \times n\} \subseteq \mathbb{Z}^k$ lattice since they…
This article is devoted to various methods (optimal transport, fixed-point, ordinary differential equations) to obtain existence and/or uniqueness of Cournot-Nash equilibria for games with a continuum of players with both attractive and…
The classical and quantum behavior of a particle inside a square box under the influence of the gravitational field is studied. Detailed calculations on periodic orbits, probability densities as well as expectation values and uncertainties…
The Rock-Scissors-Paper game has been studied to account for cyclic behaviour under various game dynamics. We use a two-person parametrised version of this game. The cyclic behaviour is observed near a heteroclinic cycle, in a heteroclinic…
An analysis of several important aspects of competition or conflict in games, social choice and decision theory is presented. Inherent difficulties and complexities in cooperation are highlighted. These have over the years led to a certain…
The aim of this paper is to discuss in some detail the two different quantum schemes for duopoly problems. We investigate under what conditions one of the schemes is more reasonable that the other one. Using the Cournot's duopoly example we…
The Game of Cycles, introduced by Su (2020), is played on a simple connected planar graph together with its bounded cells, and players take turns marking edges with arrows according to a sink-source rule that gives the game a topological…
We study a game-theoretic variant of the maximum circulation problem. In a flow allocation game, we are given a directed flow network. Each node is a rational agent and can strategically allocate any incoming flow to the outgoing edges.…
The class of weakly acyclic games, which includes potential games and dominance-solvable games, captures many practical application domains. In a weakly acyclic game, from any starting state, there is a sequence of better-response moves…
Traditional game theory assumes that the players in the game are aware of the rules of the game. However, in practice, often the players are unaware or have only partial knowledge about the game they are playing. They may also have…
Colonel Blotto games with discrete strategy spaces effectively illustrate the intricate nature of multidimensional strategic reasoning. This paper studies the equilibrium set of such games where, in line with prior experimental work, the…
Tian Ji's horse racing strategy, a famous Chinese legend, constitutes a promising concept to be applied to important issues in today's competitive environment; this strategy is elaborated on and analyzed by examining the general case. The…
We study the evolutionary stability of Nash equilibria (NE) in a symmetric quantum game played by the recently proposed scheme of applying `identity' and `Pauli spin flip' operators on the initial state with classical probabilities. We show…
We consider evolutionary games in which the agent selected for update compares their payoff to q neighbours, rather than a single neighbour as in standard evolutionary game theory. Through studying fixed point stability and fixation times…
The Grundy number of an impartial game G is the size of the unique Nim heap equal to G. We introduce a new variant of Nim, Restricted Nim, which restricts the number of stones a player may remove from a heap in terms of the size of the…
Dimensionality reduction is ubiquitous in analysis of complex dynamics. The conventional dimensionality reduction techniques, however, focus on reproducing the underlying configuration space, rather than the dynamics itself. The constructed…
This paper presents a study of restricted Nim with a pass. In the restricted Nim considered in this study, two players take turns and remove stones from the piles. In each turn, when the number of stones is m, each player is allowed to…
In this paper, Nash equilibrium seeking among a network of players is considered. Different from many existing works on Nash equilibrium seeking in non-cooperative games, the players considered in this paper cannot directly observe the…
Positions of chess players in intransitive (rock-paper-scissors) relations are considered. Namely, position A of White is preferable (it should be chosen if choice is possible) to position B of Black, position B of Black is preferable to…