Related papers: Games in the matrix

Every state on the algebra $M_n$ of complex nxn matrices restricts to a state on any matrix system. Whereas the restriction to a matrix system is generally not open, we prove that the restriction to every *-subalgebra of $M_n$ is open. This…

Let A, B, C, D be given finite sets of pairs of n-by-n complex matrices. We describe an algorithm to determine, with finitely many computations, whether there is a single unitary matrix U such that each pair of matrices in A is unitarily…

We define a general framework of partition games for formulating two-player pebble games over finite structures. We show that one particular such game, which we call the invertible-map game, yields a family of polynomial-time approximations…

In these notes we focus a bit on the complex case for some families of matrices and equivalences between them.

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…

This thesis is basically devoted to matroids -- fundamental structure of combinatorial optimization -- though some of our results concern simplicial complexes, or Euclidean spaces. We study old and new problems for these structures, with…

With increasing game size, a problem of computational complexity arises. This is especially true in real world problems such as in social systems, where there is a significant population of players involved in the game, and the complexity…

We study a class of algebras we regard as generalized Rock-Paper-Scissors games. We determine when such algebras can exist, show that these algebras generate the varieties generated by hypertournament algebras, count these algebras, study…

We present an algebraic framework for the analysis of combinatorial games. This framework embraces the classical theory of partizan games as well as a number of misere games, comply-constrain games, and card games that have been studied…

This is an exercise based approach to matrix groups. The idea is to collect a bunch of exercises at one place which anyone with basic knowledge of linear algebra can attempt to solve and learn matrix groups and algebraic groups.

We present an index theory of equilibria for extensive form games. This requires developing an index theory for games where the strategy sets of players are general polytopes and their payoff functions are multiaffine in the product of…

We obtain the symmetry algebra of multi-matrix models in the planar large N limit. We use this algebra to associate these matrix models with quantum spin chains. In particular, certain multi-matrix models are exactly solved by using known…

We introduce parallelism into the basic algebra of games to model concurrent game algebraically. Parallelism is treated as a new kind of game operation. The resulted algebra of concurrent games can be used widely to reason the parallel…

The following four classes of computational problems are equivalent: solving matrix games, solving linear programs, best $l^{\infty}$ linear approximation, best $l^1$ linear approximation.

We provide sufficient conditions for systems of polynomial equations over general (real or complex) algebras to have a solution. This generalizes known results on quaternions, octonions and matrix algebras. We also generalize the…

In this work, we present algebraic results concerning the combined matrices $\mathcal{C}(A)$, where the entries of $A$ belong to a number field $K$ and $A$ is a non-singular matrix. In other words, $A$ is a $n\times n$ matrix belonging to…

In the paper the main attention is paid to conditions on algebras from a given variety which provide coincidence of their algebraic geometries. The main part here play the notions mentioned in the title of the paper.

Matching games naturally generalize assignment games, a well-known class of cooperative games. Interest in matching games has grown recently due to some breakthrough results and new applications. This state-of-the-art survey provides an…

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…

We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex…