Related papers: Chess Pure Strategies are Probably Chaotic
Automatic chess problem or puzzle composition typically involves generating and testing various different positions, sometimes using particular piece sets. Once a position has been generated, it is then usually tested for positional…
Game theory is the standard tool used to model strategic interactions in evolutionary biology and social science. Traditional game theory studies the equilibria of simple games. But is traditional game theory applicable if the game is…
Consider concurrent, infinite duration, two-player win/lose games played on graphs. If the winning condition satisfies some simple requirement, the existence of Player 1 winning (finite-memory) strategies is equivalent to the existence of…
We analyse the computational complexity of finding Nash equilibria in simple stochastic multiplayer games. We show that restricting the search space to equilibria whose payoffs fall into a certain interval may lead to undecidability. In…
We study the problem of checking for the existence of constrained pure Nash equilibria in a subclass of polymatrix games defined on weighted directed graphs. The payoff of a player is defined as the sum of nonnegative rational weights on…
Predicting player behavior in strategic games, especially complex ones like chess, presents a significant challenge. The difficulty arises from several factors. First, the sheer number of potential outcomes stemming from even a single…
It has long been believed that Chess is the \emph{Drosophila} of Artificial Intelligence (AI). Studying Chess can productively provide valid knowledge about complex systems. Although remarkable progress has been made on solving Chess, the…
We consider a general time-inconsistent stochastic linear-quadratic differential game. The time-inconsistency arises from the presence of quadratic terms of the expected state as well as state-dependent term in the objective functionals. We…
Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic…
Self-play is a technique for machine learning in multi-agent systems where a learning algorithm learns by interacting with copies of itself. Self-play is useful for generating large quantities of data for learning, but has the drawback that…
In this article, we study the decision-making process of chess players by using a chess engine to evaluate the moves across different pools of games. We quantified the decisiveness of each move during the games using a metric derived from…
Suppose some cleverness score parameter is sufficiently interesting to be defined and then measured, perhaps for different strata of specialists or for the broader population. Such phenomena could have Gaussian distributions, when it comes…
We consider a game in which the action set of each player is uncountable, and show that, from weak assumptions on the common prior, any mixed strategy has an approximately equivalent pure strategy. The assumption of this result can be…
Fog of War chess is a popular variant of classical chess, in which both players have only partial information about the position of the opponent's pieces. This study provides the first theoretical analysis of endgames in Fog of War chess.…
Poker is a large complex game of imperfect information, which has been singled out as a major AI challenge problem. Recently there has been a series of breakthroughs culminating in agents that have successfully defeated the strongest human…
If you are given a simple three-dimensional autonomous quadratic system that has only one stable equilibrium, what would you predict its dynamics to be, stable or periodic? Will it be surprising if you are shown that such a system is…
Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…
From sports to science, the recent availability of large-scale data has allowed to gain insights on the drivers of human innovation and success in a variety of domains. Here we quantify human performance in the popular game of chess by…
Discrete-time replicator map is a prototype of evolutionary selection game dynamical models that have been very successful across disciplines in rendering insights into the attainment of the equilibrium outcomes, like the Nash equilibrium…
The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our…