Abstract
We provide several generalizations of the various equilibrium existence results in Reny (Econometrica 67:1029–1056, 1999), Barelli and Meneghel (Econometrica 81:813–824, 2013), and McLennan et al. (Econometrica 79:1643–1664, 2011). We also provide an example demonstrating that a natural additional generalization is not possible. All of the theorems yielding existence of pure-strategy Nash equilibria here are stated in terms of the players’ preference relations over joint strategies. Hence, in contrast to much of the previous work in the area, the present results for pure-strategy equilibria are entirely ordinal.
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