Nash Equilibrium

I've been asked to find the Nash Equilibria in a non-cooperative dynamic game. I know how to solve this if both players have two strategies, however player 1, for example, has strategy set (a,b,c) with player 2 having strategy set (l,r).

Would I be correct in setting out the table to find the NE like so



I've filled in the pay-offs and tried to find the NE as normal, but it didn't work out. Where have I gone wrong?

why are there strategy sets lll/rrr etc? is it a repeated game? if not, then you need to set it up in the same way as a 2 strategy game but with three strategies for player 1, like this (sorry for the rubbish diagram)

l r

a

b

c

Lol, I'm lost. The players move in order player 1 followed by player 2.

the diagram before making a table looks like this



so I thought that is how the table is formed, if iirc from how I was taught. So for example, the first column shows (A,l), (B,l) and (C,l), second column is (A,l), (B,l) and (C,r). This is how I thought it would work but not entirely sure.

yea, you are right in your last paragraph, but your table doesn't show the same thing. you need two columns (l,r) for player 2 and three rows (a,b,c) for player 1, so 6 boxes in total.

I've filled in the pay-offs and tried to find the NE as normal, but it didn't work out. Where have I gone wrong?