Simplicial Variable Dimension Algorithms for Solving the Nonlinear Complementarity Problem on a Product of Unit Simplices Using a General Labelling

Abstract

This paper deals with the nonlinear complementarity problem on the product space of unit simplices, S. A simplicial variable dimension algorithm developed by van der Laan and Talman for proper labellings of S is extended to the case of general labellings. General labellings allow a more natural description of the complementarity problem on the boundary of S. A distinctive feature of the new algorithm is that lower dimensional simplicial movement can occur both on the boundary and in the interior of S. In contrast, the van der Laan and Talman algorithm for proper labellings of S allows lower dimensional simplicial movement only in the interior of S. Computational experiments confirm the usefulness of general labellings for solving nonlinear complementarity problems.

Computing Nash Equilibria of Action-Graph Games via Support Enumeration

“…One is that it is the only known method for finding small-support equilibria. Another is that it has been shown to achieve better empirical performance than the previous state-of-the-art algorithms for the sample equilibrium problem, simplicial subdivision (SimpDiv) [10] and the global Newton method (GNM) [7], on many game families of interest. Notably, most of these games had pure-strategy Nash equilibria (PSNEs), which SEM finds in polynomial time.…”

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