ECON2070 INTRODUCTION TO STRATEGIC THINKING
INTRODUCTION TO STRATEGIC THINKING
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: THEend8_
ECON2070 INTRODUCTION TO STRATEGIC THINKING
SUGGESTED ANSWERS TO TUTORIAL EXERCISE 2
METIN UYANIK
1. The following payoff matrix is a possible representation. Other utility numbers
work as well, provided that the comparisons across cells (for the same player) are
the same.
Boxing Opera
Boxing 3,1 0,0
Opera 0,0 1,3
Note: As you can guess, the preferences of the players were reversed before
“equity and diversity” has taken its contemporary meaning. Quite a number of
textbooks changes either the name of the game, or the name of the choices each
player have (to be less gender-suggestive) to be politically correct. Still, most
game theorists continue to refer to this game as the Battle of the Sexes, and the
“Boxing” and “Opera” actions are still the default to many.
2. (Pollution)
(a) This game is given by:
T D T D
T 3,3,3 3,4,3 T 3,3,4 0,1,1
D 4,3,3 1,1,0 D 1,0,1 1,1,1
T D
(b) No. Consider Firm 1. If both Firms 2 and 3 are Treating, Dumping is the
only best response. But if only one other firm is Treating, Treating is the
only best response. Therefore neither action can dominate the other. The
three firms are symmetric so the cases for the other two firms are the same.
3. False. If strategy a of agent i is weakly dominant, then for each strategy b ̸= a of
agent i, there exists a strategy s of the opponent such that (b, s) yields a payoff
to agent i that is strictly less than the payoff (a, s) yields to agent i. That is,
no other strategy of agent i yields the same payoff as strategy a to player i. In
particular, the comparison does not require the opponent strategy to be fixed for
all other strategy of player i.
1
4. First, eliminate B, which is strongly dominated by M . Then eliminate C which
is strongly dominated by L. Then eliminate T which is strongly dominated by
M . Then eliminate R which is strongly dominated by L. The outcome of the
elimination is (M,L).