Geodesic
On the convergence of the Lemke--Howson algorithm for bi-matrix games
Contemporary Mathematics and Its Applications, Tome 95 (2015), pp. 100-113.

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We discuss conditions that guarantee the convergence of the computational Lemke–Howson algorithm for the solution of bi-matrix games and the computation of all Nash equilibria. An example is also presented. 
@article{CMA_2015_95_a11,
     author = {D. S. Nabatova},
     title = {On the convergence of the {Lemke--Howson} algorithm for bi-matrix games},
     journal = {Contemporary Mathematics and Its Applications},
     pages = {100--113},
     publisher = {mathdoc},
     volume = {95},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMA_2015_95_a11/}
}
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D. S. Nabatova. On the convergence of the Lemke--Howson algorithm for bi-matrix games. Contemporary Mathematics and Its Applications, Tome 95 (2015), pp. 100-113. http://geodesic.mathdoc.fr/item/CMA_2015_95_a11/