Smoothing Techniques for Computing Nash Equilibria of Sequential Games

Authors:
Samid Hoda;Andrew Gilpin;Javier Peòa;Tuomas Sandholm
Affiliations:
Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213;Computer Science Department, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213;Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213;Computer Science Department, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
Venue:
Mathematics of Operations Research
Year:
2010

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Abstract

We develop first-order smoothing techniques for saddle-point problems that arise in finding a Nash equilibrium of sequential games. The crux of our work is a construction of suitable prox-functions for a certain class of polytopes that encode the sequential nature of the game. We also introduce heuristics that significantly speed up the algorithm, and decomposed game representations that reduce the memory requirements, enabling the application of the techniques to drastically larger games. An implementation based on our smoothing techniques computes approximate Nash equilibria for games that are more than four orders of magnitude larger than what prior approaches can handle. Finally, we show near-linear further speedups from parallelization.