example of Nash equilibrium
Consider the first two games given as examples of normal form games.
In Prisoner’s Dilemma the only Nash equilibrium is for both players to play : it’s apparent that, no matter what player plays, player does better playing , and vice-versa for .
Battle of the Sexes has three Nash equilibria. Both and are Nash equilibria, since it should be clear that if player expects player to play , player does best by playing , and vice-versa, while the same situation holds if player expects player to play . The third is a mixed equilibrium; player plays with probability and player plays with probability. We confirm that these are equilibria by testing the first derivatives (if then the strategy is either maximal or minimal). Technically we also need to check the second derivative to make sure that it is a maximum, but with simple games this is not really necessary.
Let player play with probability and player plays with probability .
And indeed the derivatives are at and .
|Title||example of Nash equilibrium|
|Date of creation||2013-03-22 12:52:48|
|Last modified on||2013-03-22 12:52:48|
|Last modified by||Henry (455)|