The problem presented is an augmented ver of matching pennies so P1 gets doubled payoffs for picking heads (we are given this matrix so assume this is correct).
| Heads | Tails | |
|---|---|---|
| Heads | (2,-2) | (2,-2) |
| Tails | (-1,1) | (1,-1) |
One of the questions regarding this game is about finding the Maxmin value for P1. I was a bit lost on the explanation in class & I've been trying to figure out how to calculate it from online explanations. So I've been trying to follow this explanation of Maxmin values for reference: https://www.youtube.com/watch?v=sx9cWFLDFmw
Following the method explained in the video i calculated the utilies of P1:
- U1(player 2 plays H) = 3p-1
- U1(player 2 plays T) = 1-3p
& then make 3p-1=1-3p
but I think this is where I get confused. So then I get 6p-1=1... essentially so 6p=2 and getting p=1/3.
The final step is apparenly plugging this p value back into either of the utilities:
- U1(player 2 plays H) = 3p-1 = 3(1/3)-1
- U1(player 2 plays T) = 1-3p = 1-3(1/3)
But doing so gives me 0
In the example from our class, the result for regular matching pennies was 1/2 which I still am not sure how that was worked out...
| Heads | Tails | |
|---|---|---|
| Heads | (1,-1) | (1,-1) |
| Tails | (-1,1) | (1,-1 |
Can anyone help clarify my gaps in knowledge? I am sorry if these are silly questions but I am doing my first module in Game Theory so a lot of this takes a bit of time to sink in. Thanks!