I wake up in the night and take the pie , you sleep : I win all the pie , you lose it all (1,0)Clearly, a good outcome for both is sharing the pie as we each get 0.5 , 0.5
I wake up in the night, you too : we fight over the pie and smash it in the process, we both loose (0,0)
You wake up , I sleep : ( 0 for me ,1 for you)
We both sleep and the following morning we cut the pie in half ( 0.5 , 0.5)
the Nash equilibrium (named after John Forbes Nash, who proposed it) is a solution concept of a game involving two or more players, in which no player has anything to gain by changing only his or her own strategy unilaterally. If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium.I can't just choose to sleep, cause if you don't choose to sleep as well I will lose all the pie. You think like me, so you will also keep your decision and go during night. It seems like a nash equilibrium to me, cause nobody benefits if we both choose not to change our decision. The dilemma is "solved" by using probability estimation, as we aren't really equal and we don't have access to the same information at all times.
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posted by Burhanistan at 8:27 PM on March 21, 2008