Generic finiteness of equilibrium distributions for bimatrix outcome game forms

We provide sufficient and necessary conditions for the generic finiteness of the number of distributions on outcomes, induced by the completely mixed Nash equilibria associated to a bimatrix outcome game form. These equivalent conditions are stated in terms of the ranks of two matrices constructed from the original game form.The first author acknowledges that this work was supported by a grant of the Romanian National Authority for Scientific Research and Innovation, CNCS-UEFISCDI, project number PN-II-RU-TE-2014-4-1827. The second author acknowledges financial support from the Ministerio Economía y Competitividad (Spain), grant ECO2016-75992-P, MDM 2014-0431, and Comunidad de Madrid, MadEco-CM (S2015/HUM-3444). The third author acknowledges support from the Spanish Ministerio de Economía y Competitividad under project ECO2015-66803-P and from the Danish Council for Independent Research|Social Sciences (Grant-id: DFFD 1327-00097)