Column
Left Right
Up -1,-1 -10,0
ROW
Down 0, -10 -8, -8
1.4 Do you recognize this game from your reading or the lecture?
You can do a linear transformation on the
payoffs of a game without changing its essential structure. In
fact, you can even do more general monotonic
transformations, though that will affect the probabilities in a
mixed strategy equilibrium. Which game is disguised under the
action names of Game 1? For the answer, click here
A positive monotonic transformation take each payoff combination X, Y and transforms it to f(x), f(Y), where the function f is such that if a is greater than b, then f(a) is greater than f(b). Linear transformations are monotonic, but so are others. For example, apply the transformation f(x) = (x+10) squared to Game 1: GAME 1b
Column
Left Right
Up 81,81 0,100
ROW
Down 100, 0 4,4
Game 1b and Game 1 are essentially the same.
Return to Self Test 1.