On equilibrium points in bimatrix games

By H. Kuk. 1996

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Citations in the corpus

Empirically Evaluating Multiagent Learning Algorithms (2014, methodology): “If there are any equilibria that are still tied we use the one found ﬁrst by GAMBIT’s implementation of Lemke-Howson.”
Mean Field Multi-Agent Reinforcement Learning (2018, methodology): “…an iterative procedure with two alternating steps for computing the Nash policy: 1) solving the Nash equilibrium of the current stage game deﬁned by { Q t } using the Lemke-Howson algorithm (Lemke & Howson, 1964), 2) improving the estimation of the Q -function with the new Nash equilibrium value.”
Nash equilibria in random games (2005, background): “[12]; a proof that the Lemke-Howson algorithm [18] takes exponential time with all possible initial pivots [26].”
Comparative evaluation of MAL algorithms in a diverse set of ad hoc team problems (2012, unknown): “For a selection, see [3–6 , 15– 17, 21– 24 ,32 ].”
Robust game theory (2006, background): “Traditionally, the favored algorithm for two-player, non-fixed-sum, finite games with complete information has been the Lemke-Howson path-following algorithm [31] for linear complementarity problems.”
Limit Analysis of Frictional Block Assemblies as a Mathematical Program With Complementarity Constraints (2001, methodology): “However, adaptations of Lemke's method [15], the standard technique for linear complementarity problems, is only known to process (7) when V = N.”
Complementarity problems in GAMS and the PATH solver 1 This material is based on research supported (2000, methodology): “In particular, PATH can emulate Lemke’s method [5, 27] for LCP with the following options:”
The complexity of computing a Nash equilibrium (2006, methodology): “In the context of games, the Lemke-Howson algorithm [18] computes a Nash equilibrium for 2-player games by following a similar end of the line path.”
Algorithm for cardinality-constrained quadratic optimization (2009, methodology): “Motivated by this work, we extend the algorithm of [4] by using Lemke’s pivoting algorithm [7, 14] to solve the successive sub-problems in the branch-and-bound tree.”
Run the GAMUT: a comprehensive approach to evaluating game-theoretic algorithms (2004, methodology): “For two-player games the LemkeHowson algorithm [8] is best and is used by default in Gambit.”
Provable Self-Play Algorithms for Competitive Reinforcement Learning (2020, methodology): “We note however that there exists practical implementations of the subroutine such as the Lemke-Howson algorithm (Lemke and Howson, 1964) that can usually ﬁnd the solution efﬁciently.”