Mary and Lisa mow lawns
Lisa
Mary
15
20
15
20
Mary and Lisa are both kids living in the same area. To earn money, they mow lawns in their neighborhood.
Each can charge $15 or $20 per lawn. If they both charge $15, each will get 10 lawns to mow. IF they both
charge $20 each will get 5 lawns to mow. If one charges $15 and the other charges $20, then the less expensive
one will get 12 lawns to mow and the more expensive one will get only 3 lawns to mow.
If Mary charges $15 per lawn, she will earn a payoff of either ________( $60 or 150, $100 or 180, $60 or 100,
$150 or 180, $60 or 180, $100 or 150) depending on what price Lisa charges. If Mary charges $20 per lawn, she
will earn a payoff of either_______________( $60 or 150, $100 or 180, $60 or 100, $150 or 180, $60 or 180,
$100 or 150 depending upon what price Lisa charges.
Does Mary have a dominant strategy? _______________ (Yes, charge $15 per lawn,
No,
Yes, charge $20 per
lawn. )
Campaign Problem
Dawn
Robert
Play Clean
Attack
Pay clean
6,6
1,8
Attack
8,1
3,3
Dawn and Robert candidates running for office are trying to raise funds. In their promotional attempts,
each candidate can choose whether to attach the opponent or to refrain and keep the campaign clean. The
table above shows the payoff matrix for the candidates in this fund-raising game. The payoffs represent
the amount of $ raise by each campaign in thousands of dollars each week the game is played.
a.
What is the Nash equilibrium of this game?
b.
In equilibrium, Dawn will raise _________for her campaign and Robert will raise _______for his.
c.
IS there a different choice either of the candidates can make that would make them both better off?
______( Options - Yes, Both attack, Yes, Dawn attacks and Robert plays clean, Yes, both play clean,
Yes, Dawn plays clean and Robert attacks,
No, there is no other payoff that leaves both better off, No,
they are already playing such that payoffs are maximized)
Suppose the fame is repeated once each week for five weeks until Election Day
.
What will each candidate choose for the first round of the game_____ (Options - There is not enough info,
both will play clean, Dawn will stack and Robert will play clean, Dawn will play clean and Robert will
attack, Both will attack).
In 3
rd
round _____________(Dawn will attack and Robert will play clean, Dawn will play clean and Robert
will attack, Both will play clean, Both will attack, There is not enough info to determine)
In fifth round of the game______(Both will attack, There is not enough info to determine the choices, Dawn
will play clean and Robert will attack, Both will play clean, Dawn will attack and Robert will play clean).
d.
Now suppose that the candidates expect to play this game in future elections, not only this one. Namely
the candidates expect to play for an unknown number of rounds. In hopes of gaining more funds, Dawn
announces she will keep her campaign clean as long as her opponent Robert does that same and will
attack only if Robert attacks. She is playing “tit-for-tat: strategy and will play clean for first round and
subsequent rounds depend on opponent.
Think of candidates as two parties that can rationally expect to have candidates run against each other in
future elections. It’s safe to assume the political parties don’t know how long they will exist and
therefore don’t know how many rounds of this game will be played or when the last run will be.