Related papers: Tropical complementarity problems and Nash equilib…
Considering infinite-horizon, discrete-time, linear quadratic, N-player dynamic games with scalar dynamics, a graphical representation of feedback Nash equilibrium solutions is provided. This representation is utilised to derive conditions…
We propose a framework to compute approximate Nash equilibria in integer programming games with nonlinear payoffs, i.e., simultaneous and non-cooperative games where each player solves a parametrized mixed-integer nonlinear program. We…
In this article we study linear complementarity problem with hidden $Z$-matrix. We extend the results of Fiedler and Pt{\'a}k for the linear system in complementarity problem using game theoretic approach. We establish a result related to…
This paper deals with the complexity of the problem of computing a pure Nash equilibrium for discrete preference games and network coordination games beyond $O(\log n)$-treewidth and tree metric spaces. First, we estimate the number of…
We study the problem of computing stationary Nash equilibria in discounted perfect information stochastic games from the viewpoint of computational complexity. For two-player games we prove the problem to be in PPAD, which together with a…
Games with incomplete preferences are an important model for studying rational decision-making in scenarios where players face incomplete information about their preferences and must contend with incomparable outcomes. We study the problem…
We study the problem of computing an $\epsilon$-Nash equilibrium in repeated games. Earlier work by Borgs et al. [2010] suggests that this problem is intractable. We show that if we make a slight change to their model---modeling the players…
We know that the Nash equilibria of a game cannot be computed efficiently unless $P = PPAD$. But can they be learned? Are there dynamics that (1) can be computed efficiently by the players at each strategy profile and (2) are guaranteed to…
Two-player complete-information game trees are perhaps the simplest possible setting for studying general-sum games and the computational problem of finding equilibria. These games admit a simple bottom-up algorithm for finding subgame…
The performance of two pivoting algorithms, due to Lemke and Cottle and Dantzig, is studied on linear complementarity problems (LCPs) that arise from infinite games, such as parity, average-reward, and discounted games. The algorithms have…
We study Markov perfect equilibria in continuous-time dynamic games with finitely many symmetric players. The corresponding Nash system reduces to the Nash-Lasry-Lions equation for the common value function, also known as the master…
We apply methods and techniques of tropical optimization to develop a new theoretical and computational framework for the implementation of the Analytic Hierarchy Process in multi-criteria problems of rating alternatives from pairwise…
We consider the problem of computing mixed Nash equilibria of two-player zero-sum games with continuous sets of pure strategies and with first-order access to the payoff function. This problem arises for example in game-theory-inspired…
Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet…
Many efficient algorithms have been designed to recover Nash equilibria of various classes of finite games. Special classes of continuous games with infinite strategy spaces, such as polynomial games, can be solved by semidefinite…
Game theory has emerged as a powerful framework for modeling a large range of multi-agent scenarios. Many algorithmic solutions require discrete, finite games with payoffs that have a closed-form specification. In contrast, many real-world…
In this paper, we aim to design a distributed approximate algorithm for seeking Nash equilibria of an aggregative game. Due to the local set constraints of each player, projectionbased algorithms have been widely employed for solving such…
A general issue in computational optimization is to develop combinatorial algorithms for semidefinite programming. We address this issue when the base field is nonarchimedean. We provide a solution for a class of semidefinite feasibility…
The recently defined class of integer programming games (IPG) models situations where multiple self-interested decision makers interact, with their strategy sets represented by a finite set of linear constraints together with integer…
A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…