Re:Complexity Theory, Game Theory, and Economics
by bluetwo on Saturday January 06, 2018 @01:43PM
(#16086752)
Presuming the existence of E.S.P. or a time machine, that all checks out.
Otherwise you have a little bit of a problem related to when and how you know the strategy executed by your opponent.
On paper you can get around this issue by ignoring the time element, but in actual execution with humans or intelligent agents, the problem exists.
If all players write down the strategy they are going to play on a sheet of paper and show them to all other players (can include randomisation) then no player would have a strict incentive to alter their strategy.
With rock paper scissors, if me and my opponent both write down 1/3,1/3,1/3 randomisation, then neither of us would strictly benefit from doing something else.
Your [1/3,1/3,1/3], [1,0,0] is not a Nash Equilibrium. Whilst the second player does not have a strict incentive to change strategies, the first player can switch to [0,0,1] and win every time.