New BERG Working Paper No. 191 of Florian Herold and Christoph Kuzmics published

In the BERG Working Paper Series Florian Herold and Christoph Kuzmics have published a new paper (No 191) entitled "Farkas' Lemma and Complete Indifference".

A complete overview of all BERG Working Papers published so far can be found here.



In a finite two player game consider the matrix of one player's payoff difference between any two consecutive pure strategies. Define the half space induced by a column vector of this matrix as the set of vectors that form an obtuse angle with this column vector. We use Farkas' lemma to show that this player can be made indifferent between all pure strategies if and only if the union of all these half spaces covers the whole vector space. This result leads to a necessary (and almost sufficient) condition for a game to have a completely mixed Nash equilibrium. We demonstrate its usefulness by providing the class of all symmetric two player three strategy game that have a unique and completely mixed symmetric Nash equilibrium.