Related papers: On Matrix Method of Symmetric Games

We present a new variant of the potential game and show that certain compact subsets of $\R^n$, including a large class of self-affine sets, are winning in our game. We prove that sets with sufficiently strong winning conditions are…

Zero-sum and non-zero-sum (aka general-sum) games are relevant in a wide range of applications. While general non-zero-sum games are computationally hard, researchers focus on the special class of monotone games for gradient-based…

Candogan et al. (2011) provide an orthogonal direct-sum decomposition of finite games into potential, harmonic and nonstrategic components. In this paper we study the issue of decomposing games that are strategically equivalent from a…

Game balancing is an important part of the (computer) game design process, in which designers adapt a game prototype so that the resulting gameplay is as entertaining as possible. In industry, the evaluation of a game is often based on…

Theory interpolation has found several successful applications in model checking. We present a novel method for computing interpolants for ground formulas in the theory of equality. The method produces interpolants from colored congruence…

This paper studies how to efficiently update the saddle-point strategy, or security strategy of one player in a matrix game when the other player develops new actions in the game. It is well known that the saddle-point strategy of one…

We study the symmetric outer product decomposition which decomposes a fully (partially) symmetric tensor into a sum of rank-one fully (partially) symmetric tensors. We present iterative algorithms for the third-order partially symmetric…

We consider the problem of solving linear least squares problems in a framework where only evaluations of the linear map are possible. We derive randomized methods that do not need any other matrix operations than forward evaluations,…

In two player bi-matrix games with partial monitoring, actions played are not observed, only some messages are received. Those games satisfy a crucial property of usual bi-matrix games: there are only a finite number of required (mixed)…

We focus on the design of algorithms for finding equilibria in 2-player zero-sum games. Although it is well known that such problems can be solved by a single linear program, there has been a surge of interest in recent years for simpler…

A new class of projected dynamical systems of third order is investigated for quasi (parametric) variational inequalities in which the convex set in the classical variational inequality also depends upon the solution explicitly or…

We introduce the novel notion of winning cores in parity games and develop a deterministic polynomial-time under-approximation algorithm for solving parity games based on winning core approximation. Underlying this algorithm are a number…

This paper provides effective methods for the polyhedral formulation of impartial finite combinatorial games as lattice games. Given a rational strategy for a lattice game, a polynomial time algorithm is presented to decide (i) whether a…

Many analysis and verifications tasks, such as static program analyses and model-checking for temporal logics reduce to the solution of systems of equations over suitable lattices. Inspired by recent work on lattice-theoretic progress…

We introduce several methods of decomposition for two player normal form games. Viewing the set of all games as a vector space, we exhibit explicit orthonormal bases for the subspaces of potential games, zero-sum games, and their orthogonal…

Stochastic games are a convenient formalism for modelling systems that comprise rational agents competing or collaborating within uncertain environments. Probabilistic model checking techniques for this class of models allow us to formally…

We consider a sub-class of bi-matrix games which we refer to as two-person (hereafter referred to as two-player) additively-separable sum (TPASS) games, where the sum of the pay-offs of the two players is additively separable. The row…

Evolutionary game theory studies populations that change in response to an underlying game. Often, the functional form relating outcome to player attributes or strategy is complex, preventing mathematical progress. In this work, we…

We are interested in finding a solution to the tensor complementarity problem with a strong M-tensor, which we call the M-tensor complementarity problem. We propose a lower dimensional linear equation approach to solve that problem. At each…

This paper provides a decomposition technique for the purpose of simplifying the solution of certain zero-sum differential games. The games considered terminate when the state reaches a target, which can be expressed as the union of a…