H.G.Muller:
| Note that a Nash equilibrium in a symmetric zero-sum game must be the
| globally optimum strategy.

Chess isn't entirely symmetric, since there is in general a small advantage of making the first move. But for players (or games) adhering to a piece value theory throughout as a main deciding factor, perhaps such balance may occur. The only world champion that was able to do that, winning by playing with very small positional and material advantages, was perhaps Karpov. Kasparov learned to break through that heavily positional playing, in part by training against the Swedish GM Andersson who specialized in a similar hyper-defensive playing. A more normal way of winning is at some point making material sacrifices in exchange for strong initiative particularly combined with a mating attack, and then winning by either succeeding by a mate or via some material gains neutralizing to a winning end-game. Perhaps when determining piece values, such games should be excepted. And since computers are not very good at such strategies, perhaps such game exclusion occurs naturally when letting computers playing against themselves.