I wake up in the night and take the pie , you sleep : I win all the pie , you lose it all (1,0)
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.
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