Related papers: Dimension and codimension of simple games
The Minority Game is a simple yet highly non-trivial agent-based model for a complex adaptive system. Despite its importance, a quantitative explanation of the game's fluctuations which applies over the entire parameter range of interest…
This paper is concerned with complexity theoretic aspects of a general formulation of quantum game theory that models strategic interactions among rational agents that process and exchange quantum information. In particular, we prove that…
We introduce and investigate a range of general notions of a game. Our principal notion is based on a set of agents modifying a relational structure in a discrete evolution sequence. We also introduce and study a variety of ways to model…
Topics concerning metric dimension related invariants in graphs are nowadays intensively studied. This compendium of combinatorial and computational results on this topic is an attempt of surveying those contributions that are of the…
Minority game is a model of heterogeneous players who think inductively. In this game, each player chooses one out of two alternatives every turn and those who end up in the minority side wins. It is instructive to extend the minority game…
Many important values for cooperative games are known to arise from least square optimization problems. The present investigation develops an optimization framework to explain and clarify this phenomenon in a general setting. The main…
Representation languages for coalitional games are a key research area in algorithmic game theory. There is an inherent tradeoff between how general a language is, allowing it to capture more elaborate games, and how hard it is…
We consider two-player games played on weighted directed graphs with mean-payoff and total-payoff objectives, two classical quantitative objectives. While for single-dimensional games the complexity and memory bounds for both objectives…
Recent advancements in algorithms for sequential decision-making under imperfect information have shown remarkable success in large games such as limit- and no-limit poker. These algorithms traditionally formalize the games using the…
A proposal in a weighted voting game is accepted if the sum of the (non-negative) weights of the "yea" voters is at least as large as a given quota. Several authors have considered representations of weighted voting games with minimum sum,…
We present a new tool for the study of multiplayer stochastic games, namely the modified game, which is a normal-form game that depends on the discount factor, the initial state, and for every player a partition of the set of states and a…
We study the structure of the underlying network of connections in the Minority Game. There is not an explicit interaction among the agents, but they interact via global magnitudes of the model and mainly through their strategies. We define…
We establish a relationship between the word complexity and the number of generalized diagonals for a polygonal billiard. We conclude that in the rational case the complexity function has cubic upper and lower bounds. In the tiling case the…
We present a unifying representation of computation as a two-player game between an \emph{Algorithm} and \emph{Nature}, grounded in domain theory and game theory. The Algorithm produces progressively refined approximations within a Scott…
This short note is devoted to the unraveling of the hidden interactivity of ordinary games which is an artefact of predictions of the behaviour of other players by the fixed player and describes deviations of their real behaviour from such…
This study investigates simple games. A fundamental research question in this field is to determine necessary and sufficient conditions for a simple game to be a weighted majority game. Taylor and Zwicker (1992) showed that a simple game is…
Simplicial complexes describe collaboration networks, protein interaction networks and brain networks and in general network structures in which the interactions can include more than two nodes. In real applications, often simplicial…
In this paper we discuss various aspects of the problem of determining the minimal dimension of an injective linear representation of a finite semigroup over a field. We outline some general techniques and results, and apply them to…
This work contains the mathematical exploration of a few prototypical games in which central concepts from statistics and probability theory naturally emerge. The first two kinds of games are termed Fisher and Bayesian games, which are…
High-dimensional data and high-dimensional representations of reality are inherent features of modern Artificial Intelligence systems and applications of machine learning. The well-known phenomenon of the "curse of dimensionality" states:…