What’s the utility of going to the state where I have one bullet and the opponent has none? If I try to do the matrix for that, I get this:
What’s the utility of going to the state where I have one bullet and the opponent has none?
If I try to do the matrix for that, I get this:
This made me think the last table was just for the (1,0) state. Is this not the case?
I’m not sure why the previous state would matter.
By previous state, I meant current. I misspoke.
Yes, the last table is for the (1,0) table.
So the utility for S+B is 0 and the utility for R+R is 0.5. The equilibrium is where both players reload with probability = 2⁄3. The utility of the (1,0) state is +2/3.
Thanks. I now see my mistake. I shouldn’t have subtracted the expected utility of the current state from the expected utility of the next.
This made me think the last table was just for the (1,0) state. Is this not the case?
I’m not sure why the previous state would matter.
By previous state, I meant current. I misspoke.
Yes, the last table is for the (1,0) table.
So the utility for S+B is 0 and the utility for R+R is 0.5. The equilibrium is where both players reload with probability = 2⁄3. The utility of the (1,0) state is +2/3.
Thanks. I now see my mistake. I shouldn’t have subtracted the expected utility of the current state from the expected utility of the next.