Related papers: The relation between eigenvalue/eigenvector and ma…

Using methods from the statistical mechanics of disordered systems we analyze the properties of bimatrix games with random payoffs in the limit where the number of pure strategies of each player tends to infinity. We analytically calculate…

Truth, consistency and elementary equivalence can all be characterised in terms of games, namely the so-called evaluation game, the model-existence game, and the Ehrenfeucht-Fraisse game. We point out the great affinity of these games to…

We consider path-connected sets of matrices and the induced paths between eigenvalues. We discuss the equivalence relation generated by these paths, and how it relates to the presence of higher multiplicity eigenvalues realized by the set.…

For matrix games we study how small nonzero probability must be used in optimal strategies. We show that for nxn win-lose-draw games (i.e. (-1,0,1) matrix games) nonzero probabilities smaller than n^{-O(n)} are never needed. We also…

Eigenvectors associated with non-degenerate eigenvalues are shown to correspond to columns of the adjugate of the characteristic matrix. Degenerate eigenvalues are associated with eigenvectors that correspond to reduced complement tensors…

Quantum games have proposed a new point of view for the solution of the classical problems and dilemmas in game theory. Certain quantization relationships can be proposed with the objective that a game can be generalized into a quantum…

Random matrices in the large N expansion and the so-called double scaling limit can be used as toy models for quantum gravity: 2D quantum gravity coupled to conformal matter. This has generated a tremendous expansion of random matrix…

This paper extends Berge's maximum theorem for possibly noncompact action sets and unbounded cost functions to minimax problems and studies applications of these extensions to two-player zero-sum games with possibly noncompact action sets…

In this paper we bring to light an unprecedented property of the eigenvalues of a matrix A with the eigenvalues and eigenvectors of a submatrix of A. This property can be used, through the technique developed here, to determine some of…

In this paper, a gentle introduction to Game Theory is presented in the form of basic concepts and examples. Minimax and Nash's theorem are introduced as the formal definitions for optimal strategies and equilibria in zero-sum and…

We provide a complete characterization for uniqueness of equilibria in unconstrained polymatrix games. We show that while uniqueness is natural for coordination and general polymatrix games, zero-sum games require that the dimension of the…

Evolutionary game theory is a common framework to study the evolution of cooperation, where it is usually assumed that the same game is played in all interactions. Here, we investigate a model where the game that is played by two…

We address the equilibrium concept of a reverse auction game so that no one can enhance the individual payoff by a unilateral change when all the others follow a certain strategy. In this approach the combinatorial possibilities to consider…

This is about algebras of complex $n\times n$ matrices. Do these algebras look similar for all large $n$? This paper is intended for general audience.

In some games, additional information hurts a player, e.g., in games with first-mover advantage, the second-mover is hurt by seeing the first-mover's move. What properties of a game determine whether it has such negative "value of…

The eigenvalues of the transfer matrix in a six-vertex model (with periodic boundary conditions) can be written in terms of n constants v1,...,vn, the zeros of the function Q(v). A peculiar class of eigenvalues are those in which two of the…

We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…

We define the distance between two information structures as the largest possible difference in value across all zero-sum games. We provide a tractable characterization of distance and use it to discuss the relation between the value of…

Standard game theory assumes that the structure of the game is common knowledge among players. We relax this assumption by considering extensive games where agents may be unaware of the complete structure of the game. In particular, they…

We introduce and study the class of semidefinite games, which generalizes bimatrix games and finite $N$-person games, by replacing the simplex of the mixed strategies for each player by a slice of the positive semidefinite cone in the space…