On the Probability of Existence of Pure Equilibria in Matrix Games

S. Mishra, Centre for Development Studies
T. K. Kumar, Indian Statistical Institute, Bangalore

Article comments

This is the authors post-peer review, accepted paper published in the 'Journal of Optimization Theory and Application'. The link to the journal web page is as follows: http://www.springerlink.com/content/pm6141670n565021/. This is also available at: http://www.control.ece.ntua.gr/papers/28.pdf.

Abstract

In a recent paper (Ref. 1), Papavassilopoulos obtained results on the probability of the existence of pure equilibrium solutions in stochastic matrix games. We report a similar result, but where the payoffs are drawn from a finite set of numbers N. In the limiting case, as N tends to infinity, our result and that of Papavassilopoulos are identical. We also cite similar results obtained independently by others, some of which were already independently brought to the notice of Papavassilopoulos by Li Calzi as reported in Papavassilopoulos (Ref. 2). We cite a much earlier result obtained by Goldman (Ref. 3). We also cite our related work (Ref. 4), in which we derive the conditions for the existence of mixed strategy equilibria in two-person zero-sum games.