Overview
Syllabus
Intro
Rank-k games
Suggested example of a rank-1 game
NE of games with parameter X
Global Newton Method [Govindan/Wilson 2003]
Rank reduction by intersection with hyperplane
works for rank 1: monotone path, unique rank-O NE
LP for zero-sum game
LP for parameterized zero-sum game
Parameterized matrix (column bonuses)
Equivalent: Parameterized objective function
"Wrap-around" hyperplane defines the path
Algorithm 1: Binary search
Algorithm 2: Enumeration
Parameterized LP [Murty 1980]
Inspired by Murty
Output efficiency
PPAD- versus NP-hardness
Taught by
Hausdorff Center for Mathematics