Related papers: Linear Representation of Symmetric Games
We develop methods to formally describe and compare games, in order to probe questions of game structure and design, and as a stepping stone to predicting player behavior from design patterns. We define a grammar-like formalism to describe…
Linearity allows several versions of reality to simultaneously exist in the state vector. But it implies that there is no interaction between versions, and that there will never be perception of more than one version. It also implies, in…
This paper presents a series of general results about the optimal estimation of physical transformations in a given symmetry group. In particular, it is shown how the different symmetries of the problem determine different properties of the…
Finite games in normal form and their mixed extensions are a corner stone of noncooperative game theory. Often generic finite games and their mixed extensions are considered. But the properties which one expects in generic games and the…
In this paper, we introduce a framework of new mathematical representation of Game Theory, including static classical game and static quantum game. The idea is to find a set of base vectors in every single-player strategy space and to…
The game in which acts of participants don't have an adequate description in terms of Boolean logic and classical theory of probabilities is considered. The model of the game interaction is constructed on the basis of a non-distributive…
Genericity is the idea that the same program can work at many different data types. Longo, Milstead and Soloviev proposed to capture the inability of generic programs to probe the structure of their instances by the following equational…
Game semantics provides an interactive point of view on proofs, which enables one to describe precisely their dynamical behavior during cut elimination, by considering formulas as games on which proofs induce strategies. We are specifically…
We study the asymptotics of representations of a fixed compact Lie group. We prove that the limit behavior of a sequence of such representations can be described in terms of certain random matrices; in particular operations on…
Many binary collective choice situations can be described as weighted simple voting games. We introduce weighted committee games to model decisions on an arbitrary number of alternatives in analogous fashion. We compare the effect of…
We explore links between the thin concurrent games of Castellan, Clairambault and Winskel, and the weighted relational models of linear logic studied by Laird, Manzonetto, McCusker and Pagani. More precisely, we show that there is an…
This paper defines a linear representation for nonlinear maps $F:\mathbb{F}^n\rightarrow\mathbb{F}^n$ where $\mathbb{F}$ is a finite field, in terms of matrices over $\mathbb{F}$. This linear representation of the map $F$ associates a…
Using the theory of representations of the symmetric group, we propose an algorithm to compute the invariant ring of a permutation group. Our approach have the goal to reduce the amount of linear algebra computations and exploit a thinner…
We study the computational complexity of finding stable outcomes in hedonic games, which are a class of coalition formation games. We restrict our attention to symmetric additively-separable hedonic games, which are a nontrivial subclass of…
Solving parity games, which are equivalent to modal $\mu$-calculus model checking, is a central algorithmic problem in formal methods. Besides the standard computation model with the explicit representation of games, another important…
We start with definitions of the general notions of the theory of $\Bbb Z_{2}$-graded algebras. Then we consider theory of inductive families of $\Bbb Z_{2}$-graded semisimple finite-dimensional algebras and its representations in the…
Network games provide a powerful framework for modeling agent interactions in networked systems, where players are represented by nodes in a graph and their payoffs depend on the actions taken by their neighbors. Extending the framework of…
The traditional mathematical model for an impartial combinatorial game is defined recursively as a set of the options of the game, where the options are games themselves. We propose a model called gamegraph, together with its generalization…
Among the strategic choices made by today's economic actors are choices about algorithms and computational resources. Different access to computational resources may result in a kind of economic asymmetry analogous to information asymmetry.…
The peculiarity of adversarial team games resides in the asymmetric information available to the team members during the play, which makes the equilibrium computation problem hard even with zero-sum payoffs. The algorithms available in the…