In the context of finite two-player games we say that a mixed strategy equilibrium is uniform if the pair (u,v) of mixed strategies is equilibrium and both u and v are uniform i.e. they assign equal probability to all the pure strategies in their support (we say that a pure strategy p is in the support of a mixed strategy m if m(p) > 0). What is it known about the conditions in general where there exists an uniform mixed strategy equilibrium?
Maybe this one could be of interest? https://www.hindawi.com/archive/2013/534875/
Perhaps when a point of unified singularity is reached with N players, irrespective of time or space constraints, or limits of the play boundary being extended - or fractally extruded - to be mutually inclusive. The state of temporary non equilibrium may be focused on, but may not completely describe the life cycles of the whole game, but rather the cyclical breathing motions of the life of the game itself. All in all, a point in time vs time point and infinity?
In such a case, in all probability the primary condition would be the state perspective of the observer. Tenet: You get what you measure.
Kjetil K. Haugen: The article is interesting, but I'm afraid that it deals with different concept i.e. with the concept of sub-game perfect NE.
Example of a game where uniform mixed strategy NE exists is the matching pennies game i.e. the pair (u,v) where u(p)=1/2 and v(p*)=1/2, for all pure strategies p, p'.
Aha, then I think I understand what you mean: You are interested in general two player finite (imperfect information?) games and under what circumstances the mixed strategy NE is uniform? I believe literature uses the term symmetric here, instead of uniform. Maybe that is the reason for my misunderstanding. It may be that necessary answers exist. For instance, take a look at http://people.math.umass.edu/~lr7q/ps_files/teaching/math456/lecture7.pdf
If not necessary generality (or pointers to it) is available in the above document, it should be relatively easy to develop it. I did something on the matter many years ago, and may dig it up if necessary :)
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