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# Nash Equilibrium Watch

1. 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?
2. (Original post by Ent24)
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
3. (Original post by thegaffer91)
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.
4. (Original post by Ent24)
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.
5. (Original post by thegaffer91)
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.
Ok, I did 6 boxes, but no NE came out of it.

6. (Original post by Ent24)
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?
First of all, your table is right.* Strategies are complete contingent set of actions showing what the agent plans to do at each information set. Since this is a sequential game where each node constitutes an own information set, your normal form version of the game is correct. The other propose form with only two strategies for player 2 would be true if and only if players moved simultaneously.

Be reminded that Nash equilibria are not restricted to pure strategies. The players may play mixed ones as well.

*but you may check whether you have all strategies. Where, for instance, is rll?
7. My second name is Nash xD
8. i know nothing about maths so this probably wont help, just i saw the title and recognised it.
i play poker and their is a nash equilibrium for playing 1v1 which tells you when u should either go all in or fold with the factors being your cards and the number of big blinds left in your stack.
anyway thats why very poor imput to the thread, if any1 wants me to explain the nash in poker or talk poker pm me

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