10:51 Can you please tell why did you take a triangle as the mixed strategy simplex of the first player? Like can't we take a 1x1x1 cube where the strategy probabilities at any point within it would be its coordinates? The triangle approach doesn't seem so obvious
10:51 Can you please tell why did you take a triangle as the mixed strategy simplex of the first player? Like can't we take a 1x1x1 cube where the strategy probabilities at any point within it would be its coordinates? The triangle approach doesn't seem so obvious
Sum of probabilities must be 1.
The triangle is effectively the region in the 1x1x1 cube where the sum of points is 1.(try graphing x1 + x2 + x3 = 1)
that means that points (2, 1) and (4, 5) are also Nash Equilibrium because 3 is played with probability 0, right?
Great Video! Is this an LCP?
Thanks and yes, the problem of finding a Nash equilibrium in a 2-player game can be reduced to a linear complementarity problem.
Hi will you continue making videos for Algorithmic Game Theory or Theoretical Computer Science?
There are a few topics in these areas that I hope to cover in future videos.
@@compscilessons That's great, please do! your channel is great, all the best!