Self-test on dominant strategies, dominated strategies, and Nash equilibrium

                                    Left         Right
                   Up           -1,-1        -10,0
                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

                                    Left                  Right
                   Up           81,81           0,100
                Down        100, 0            4,4
Game 1b and Game 1 are essentially the same.

Return to Self Test 1.

Send comments to Prof. Rasmusen. Last updated: October 27, 1996