Games of fixed rank: a hierarchy of bimatrix games

Ravi Kannan, Thorsten Theobald
2009 Economic Theory  
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 kgames 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
more » ... libria 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 εapproximation. Expressive power. The number of Nash equilibria of an m × n-bimatrix game does not only depend on m and n, but also on the entries of the payoff matrices A and B. The
doi:10.1007/s00199-009-0436-2 fatcat:srt5zgxqwbfcnppfvvwvg6qsi4