Turning Fights into Matrixes

When two people have different understandings of a payout matrix then the option that is one persons thinks are the option then it is not really an option. 

I am constantly irritating my friends by making them sit down and draw out our arguments as payout matrixes. They hate when I do this but I always have a great time. 

This weekend I was sitting on the couch with my friend and future housemate Nate when he made the “joke” that he was going to put water in my cast iron pan. Now if you have never invested in cultivating a beautifully seasoned cast iron pan you may not understand why this would be a horrible thing to do, but getting an iron pan wet will RUIN IT.   

Left is a happy pan, no water no rust, lost of oil—> Right is a UNHAPPY SAD RUSTY PAN!

I wrote out our interaction in three charts. In each chart Sophie is P1 and Nate is P2. Sophie can allow Nate to use the pan or she can no allow him to use the pan. Nate can either promise to keep water out of the pan or not. I wrote three charts out because I think me and Nate Had different understandings of each others payout values. This means the option I relived to be a possible NASH was not actually a Nash. 

This payout matrix describes my beliefs about the possible payout utilities for this argument. It was my understanding that there would be a Nash at both AW,P and NW, NP. I got a much better payout at AW,P then at NW,P. These payout values reflect the labor it would take to make sure Nate did not use the panU1(NW,P)= -1 verses the benefit I would gain in being able to trust my friend to use my pan and not get it wet U1(AW, P) =4. This is the option I fought for. I also believed that Nates payouts would be the same if he is allowed to use promise or no promise and would get the same negative value for not being promised anything. 

Sophie’s Understanding  Nate
Sophie  Promise P Not Promise P
Allow use (AW) +4, +4 -300,+4
Not allowed use (NW) -4,-4 -1,-4

This payout matrix describes Nate perception of his payoffs and mines, where his worst option is to promise but he would prefer to use. The pan. 

Nates understanding Nate
Sophie  Promise  Not Promise 
Allow use  0, -300 -1,+10
Not allowed use  0,-300 0,0

Here is the combined matrix where we use our own perceptions of payoffs for ourself. This is the true matrix and it is clear that the only possible Nast would be NW, NP

Sophie  Promise  Not Promise 
Allow use  +4, -300 -300,+10
Not allowed use  -4,-300 -1,-0

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