Applications of Algebra for Some Game Theoretic Problems

DOI10.1142/s0129054115500033zbMath1319.91016OpenAlexW2063790342MaRDI QIDQ5250276

Samaresh Chatterji, Ratnik Gandhi

Publication date: 19 May 2015

Published in: International Journal of Foundations of Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0129054115500033

zbMATH Keywords

Galois groupNash equilibriaNewton-Raphson methodpolynomial algebra

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Noncooperative games (91A10) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Numerical computation of solutions to single equations (65H05) Field arithmetic (12E30)

Cites Work

• A globally convergent algorithm to compute all Nash equilibria for \(n\)-person games
• Homotopy methods to compute equilibria in game theory
• Finding all Nash equilibria of a finite game using polynomial algebra
• Computing equilibria: a computational complexity perspective
• The number of roots of a system of equations
• The maximal number of regular totally mixed Nash equilibria
• Oddness of the number of equilibrium points: a new proof
• The development of Galois theory from Lagrange to Artin
• Algorithms in Algebraic Number Theory
• Fast Decomposition of Polynomials with Known Galois Group
• On the Efficiency of Newton's Method in Approximating All Zeros of a System of Complex Polynomials
• Computing equilibria with group actions
• Equilibrium Points of Bimatrix Games
• The Expected Number of Nash Equilibria of a Normal Form Game
• Nash equilibria in random games
• Universality of Nash Equilibria