Related papers: Rank Reduction in Bimatrix Games
Ranking is used in sport leagues to determine a champion and/or to decide on promotion/relegation of teams. Arguably, the best known ranking method relies on scores obtained by cumulating the points associated with the wins and the draws of…
In this paper, some new criteria for detecting whether a finite game is potential are proposed by solving potential equations. The verification equations with the minimal number for checking a potential game are obtained for the first time.…
We study a version of the classical zero-sum matrix game with unknown payoff matrix and bandit feedback, where the players only observe each others actions and a noisy payoff. This generalizes the usual matrix game, where the payoff matrix…
The paper explores the concept of the rank of a bicomplex matrix, delving into four distinct types of ranks and investigating conditions under which these ranks are equivalent. It also defines and analyzes the concept of idempotent row…
Strategy iteration is a technique frequently used for two-player games in order to determine the winner or compute payoffs, but to the best of our knowledge no general framework for strategy iteration has been considered. Inspired by…
Ladder tournaments are widely used to rank individuals in real-world organizations and games. Their mathematical properties however are still poorly understood. We formalize the ranking rule generated by a ladder tournament, and we show…
In this paper, we show that the low rank matrix completion problem can be reduced to the problem of finding the rank of a certain tensor.
We develop value iteration-based algorithms to solve in a unified manner different classes of combinatorial zero-sum games with mean-payoff type rewards. These algorithms rely on an oracle, evaluating the dynamic programming operator up to…
We introduce two-level discounted games played by two players on a perfect-information stochastic game graph. The upper level game is a discounted game and the lower level game is an undiscounted reachability game. Two-level games model…
A novel lower bound is introduced for the full rank probability of random finite field matrices, where a number of elements with known location are identically zero, and remaining elements are chosen independently of each other, uniformly…
The minimum rank of a graph G is the minimum rank over all real symmetric matrices whose off-diagonal sparsity pattern is the same as that of the adjacency matrix of G. In this note we present the first exact algorithm for the minimum rank…
Matrices with low-rank structure are ubiquitous in scientific computing. Choosing an appropriate rank is a key step in many computational algorithms that exploit low-rank structure. However, estimating the rank has been done largely in an…
We propose a method for low-rank semidefinite programming in application to the semidefinite relaxation of unconstrained binary quadratic problems. The method improves an existing solution of the semidefinite programming relaxation to…
Iterated regret minimization has been introduced recently by J.Y. Halpern and R. Pass in classical strategic games. For many games of interest, this new solution concept provides solutions that are judged more reasonable than solutions…
We consider the computational complexity of the question whether a certain strategy can be removed from a game by means of iterated elimination of dominated strategies. In particular, we study the influence of different definitions of…
Ranking the participants of a tournament has applications in voting, paired comparisons analysis, sports and other domains. In this paper we introduce bipartite tournaments, which model situations in which two different kinds of entity…
Define the weight of a matrix to be the number of non-zero entries. One would like to count $m$ by $n$ matrices over a finite field by their weight and rank. This is equivalent to determining the probability distribution of the weight while…
Let $\mathbf{a} = (a_{i})_{i \geq 1}$ be a sequence in a field $\mathbb{F}$, and $f \colon \mathbb{F} \times \mathbb{F} \to \mathbb{F}$ be a function such that $f(a_{i},a_{i}) \neq 0$ for all $i \geq 1$. For any tournament $T$ over $[n]$,…
Although the definition of what empathetic preferences exactly are is still evolving, there is a general consensus in the psychology, science and engineering communities that the evolution toward players' behaviors in interactive…
The rank of a graph is defined to be the rank of its adjacency matrix. A graph is called reduced if it has no isolated vertices and no two vertices with the same set of neighbors. A reduced graph $G$ is said to be maximal if any reduced…