It was Nash that proved that all finite non-cooperative games have a solution among a few other key and significant revelations of his time before he was eventually dubbed “insane”. The Nash equilibrium is also relevant here which basically comes from the realization that all such games have solutions.
The simple example we want to start with is paper rock scissors. We can see that any pattern of choosing can definitely have a counter strategy. If someone chooses 2 paper and 1 rock, the counter is 2 scissors and 1 paper. Although the game is not played like this it is helpful for the basis of understanding the GTO strategy.
Someone can put out 2/3 rock and 1/3 scissors in an otherwise random sequence and we could see that the counter would be 2/3 paper and 1/3 rock.
The obvious GTO solution here becomes to randomly put out 1/3 of each rock, paper, or scissors, and then we are exploitable. The counter to this becomes negligible for this game.
Nash has later insights into game theory and describes one possible solution to complex or cooperative games as breaking them down into finite non-cooperative parts.
The markets (we will see as a society in the future) functions just like a game. It is not so finite and not necessarily non-cooperative, however the key observation is in relation to Hayek’s incredible machine.
Lately I have learned probability and game theory through poker, which is a game that incentivizes participation by intelligent peoples. Therefore the overall skill level of the general player pool, given a fair secure industry model, will tend towards a discovery of the GTO strategy for poker.
In other words, as good poker player, I can make the assumption that as time goes by players will get better and better, and therefore these good players will trend or tend towards GTO.
This is how we will solve such a complex game of poker, that uses a deck of cards as a probability mechanism which has more permutations than atoms in the universe.
Hayek’s explanation of the markets is relevant here, especially when understood in relation to Szabo’s works, and Nash’s works on Ideal Money. Hayek’s relevant point is that the markets have incentive to discover price stability, and in terms or perspective of games and game theory it is exactly the GTO solution in relation to the complex game of the markets that we are brute force discovering as a population.
This suggestion that there IS in fact a trend towards such a solution that is going on.