On the Probability of Existence of Pure Equilibria in Matrix Games

Srijit Mishra () and Krishna Kumar

Journal of Optimization Theory and Applications, 1997, vol. 94, issue 3, No 14, 765-770

Abstract: 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.

Keywords: Pure equilibrium; matrix games; stochastic games; separation of diagonals; mixed equilibrium (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1023/A:1022669504795

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