Open AccessAn Algebraic Geometry Approach to Compute Strategically Equivalent Bimatrix Games
Author(s) -
Corrado Possieri,
João P. Hespanha
Publication year - 2017
Publication title -
ifac-papersonline
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.308
H-Index - 72
eISSN - 2405-8971
pISSN - 2405-8963
DOI - 10.1016/j.ifacol.2017.08.2019
Subject(s) - interval (graph theory) , monotone polygon , set (abstract data type) , nash equilibrium , class (philosophy) , mathematics , algebraic number , polynomial , algebraic geometry , discrete mathematics , algebra over a field , combinatorics , mathematical optimization , computer science , geometry , pure mathematics , mathematical analysis , artificial intelligence , programming language
In this paper, a class of bimatrix games having the same Nash equilibria of a given game, either in pure or in mixed policies, is characterized. Such a goal is reached by computing the set of all the polynomials that are monotone strictly increasing in a given interval and by borrowing techniques from algebraic geometry to find solutions to a set of polynomial equalities.
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