Related papers: Interactive games and representation theory
These lecture notes give an introduction to the theory of interacting particle systems. The main subjects are the construction using generators and graphical representations, the mean field limit, stochastic order, duality, and the relation…
We give an elementary introduction to our papers relating the geometry of rational homogeneous varieties to representation theory. We also describe related work and recent progress.
The point of view of these notes on the topic is to bring out the flavour that Representation Theory is an extension of the first course on Group Theory. We also emphasize the importance of the base field. These notes cover completely the…
Underlying the theory of inferences, a primary task of logic is language analysis. Such a task can be understood as depending on a general theory of representation, taking as a starting point the idea that some entities (`` representations…
The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…
In this lecture note, we introduce the basic concepts of game theory (GT), a branch of mathematics traditionally studied and applied in the areas of economics, political science, and biology, which has emerged in the last fifteen years as…
This work uses game theory as a mathematical framework to address interaction modeling in multi-agent motion forecasting and control. Despite its interpretability, applying game theory to real-world robotics, like automated driving, faces…
Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the…
When designing or analyzing multi-agent systems, a fundamental problem is responsibility ascription: to specify which agents are responsible for the joint outcome of their behaviors and to which extent. We model strategic multi-agent…
A brief review is given of the minority game, an idealized model of a market of speculative agents, and its complex many-body behaviour. Particular consideration is given to the consequences and implications of correlations between…
I give a brief introduction to particle interactions based on representations of Poincare Lie algebra. This is later generalized to interactions based on representations of the supersymmetry Lie algebra. Globally supersymmetric models with…
The preference graph is a combinatorial representation of the structure of a normal-form game. Its nodes are the strategy profiles, with an arc between profiles if they differ in the strategy of a single player, where the orientation…
Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…
The evolution of information and communication technologies has yielded the means of sharing measurements and other information in an efficient and flexible way, which has enabled the size and complexity of control applications to increase.…
The biased interaction game described the operation of systems rooted in boundedly rational interactions under conditions of scarcity. The game explored the influence of bias and demonstrated how hierarchy and inequality are emergent system…
Game theory is the mathematical framework for analyzing strategic interactions in conflict and competition situations. In recent years quantum game theory has earned the attention of physicists, and has emerged as a branch of quantum…
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…
Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The paper is devoted to the analysis of interference of quantum strategies in quantum market games.
These are lecture notes that arose from a representation theory course given by the first author to the remaining six authors in March 2004 within the framework of the Clay Mathematics Institute Research Academy for high school students,…
Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The paper presents the history, basic ideas and recent development in quantum game theory. In this…