Games of fixed rank: a hierarchy of bimatrix games
Year: 2007
Type: article
Abstract: We propose and investigate a hierarchy of bimatrix games (A, B), whose (entry-wise) sum of the pay-off matrices of the two players is of rank k, where k is a constant. We will say the rank of such a game is k. For every fixed k, the class of rank k-games strictly generalizes the class of zero-sum games, but is a very special case of general bimatrix games. We study both the expressive power and the algorithmic behavior of these games. Specifically, we show that even for k = 1 the set of Nash equilibria of these games can consist of an arbitrarily large number of connected components. While the question of exact polynomial time algorithms to find a Nash equilibrium remains open for games of fixed rank, we present polynomial time algorithms for finding an ε-approximation.
Authors: Ravi Kannan, Thorsten Theobald
Institutions: Yale University, Technische Universität Berlin
Language: English
Topic: Game Theory and Applications
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W2014217859