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 linear transformation take each payoff combination X, Y and transforms it to a+bX, a+bY. Here, let us insist that b be positive, tho a could be negative. Thus, with a=100 and b=2, the game above becomes GAME 1a

                                    Left                  Right
                   Up                98,98              80,100
                  Down               100, 80           84,84
Game 1a and Game 1 are essentially the same.

Return to Self Test 1.

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