Cool and interesting. Thank you for sharing on HN.<p>As Nash proved, under very general conditions (e.g., payoffs are finite), in every game there's always at least one equilibrium, i.e., at least one fixed point.<p>Alas, as Papadimitriou proved in the 90's, <i>finding</i> Nash equilibria is PPAD-complete.[a][b]<p>So, as games get larger and more complex -- say, with rules and payoffs that evolve over time -- finding equilibria can become... intractable: There will always exist at least one Nash equilibrium, but you'll never be able to reach it. Simulation may well be the only way to model such games.<p>---<p>[a] <a href="https://en.wikipedia.org/wiki/PPAD_(complexity)" rel="nofollow">https://en.wikipedia.org/wiki/PPAD_(complexity)</a><p>[b] There's a great intro lecture on this by Papadimitriou himself at <a href="https://www.youtube.com/watch?v=TUbfCY_8Dzs" rel="nofollow">https://www.youtube.com/watch?v=TUbfCY_8Dzs</a>