Thatcher Margaret (MT) Neil Kinnock High Road
NK
High Road
January 13, 2011 - Lecture #3 (100%, 0%)
Low Road
(50%, 50%)
Line Item Veto = Right to veto one or more specic parts of a bill (i.e. passing Urban Renewal but not Missiles) The game tree to the left, shows us the scenario between two political gures and their choice of which way to campaign.
MT
Low Road High Road (50%, 50%)
NK
Low Road (0%, 100%) Outcomes Congress President
Congress U+M N P
Veto
U+M P U
Veto Sign
3 4 1 2
3 1 4 2
Only U Only M Neither (3, 3)
M
(2, 2)
Veto
(w/o Line Item Veto) U + M = Both U = Urban Renewal M = Missiles N = Neither P = President U + M = Both U = Urban Renewal M = Missiles N = Neither P = President SB = Sign Both VU = Veto Urban Renewal VM = Veto Missiles (with Line Item Veto) ** Sometimes having more power can be a disadvantage because others (i.e. Congress) can anticipate your use of that power, and choose to do something different. **
P
Sign Veto
P
(2, 2)
Sign
(2, 2)
(1, 4)
(2, 2)
(4, 1)
Congress U+M N P
Veto SB
P U
Veto VM
(3, 3) (1, 4)
M
VU
(2, 2)
Veto
P
Sign Veto
P
(4, 1) (2, 2)
Sign
(2, 2)
(1, 4)
(2, 2)
(4, 1)
January 13, 2011 - Lecture #3 Break Out Outlaw Heavy (150, 0) (80, 20)
Sheriff
Light Outlaw
Stay In Break Out
Sheriff and Outlaw example: Heavy and Light, refer to the sentences of the Outlaw; the game is basically to see whether the outlaw will break out of jail or stay in. Les miserables by Victor Hugo (recommended reading) Backward Induction is used to solve this game
(80, 10)
Stay In (100, 30)
Homesteading/Homestead Act of 1862 Basically stated that once an individual cultivated a specic piece of land up to a certain capacity, then that land becomes that individuals property. This proved to be wasteful, in reality, because people would sometimes not make use of the land as soon as it was their property or would do this with more than one piece of land, thus wasting land by neglecting its usefulness. Simultaneous Games Dominant Strategy: that which gives the player with this strategy the highest payoff, regardless of what strategy its opponent plays; best response to all of the its opponents strategies The next example focuses on a choice that two magazines have to make regarding what cover story to put on their current, respective issues. The choice for both lies between a story on AIDS and one on the current Budget decit. Normal Form: " " "
" "
Newsweek
AIDS"" Budget " "
" " Time " "
"
" "
" "
" "
" "
AIDS "
" " " (35*, " *) 35 Budget " " (30, 70*) " " " "
Newsweek
" (70*, 30) " " (15, 15) " " " AIDS
As shown in the Normal Form depiction of the game, both players have a dominant strategy. For both of them, choosing AIDS yields them the highest payoff, regardless of what the other player will do. This means that the best response for Time is AIDS, regardless of what Newsweek will do, and the same outcome is seen from Newsweeks perspective. The same is seen in the game tree that follows:
(35*, 35*) This is the Game Tree of the same situation:
AIDS
Time
Budget
Newsweek
Budget
AIDS
(70*, 30) (30, 70*) (15, 15)
The dotted line symbolizes that Time doesnt know what Newsweeks response will be to its move, and vice versa
Budget
January 13, 2011 - Lecture #3
Now suppose, that 60% of customers preferred Time magazine and the other 40% prefer Newsweek. This changes the payoffs for when both the magazines choose the same cover story. The equation to nd the new payoffs would be as follows: Since the total payoff is 70 when both players choose AIDS, then this should be multiplied by the percentage of preference of each magazine, and the same for the total payoff of 30 when they choose Budget: 70*Preference% for Time = New Payoff " " " New depiction of game in Normal Form: " " " " " " " " " " " Newsweek (AIDS, AIDS) = for Time: 70*60% = 42 "" " " AIDS" Budgets " " for Newsweek: 70*40% = 28 (42*, 28) (70*, 30*) " " " " " " " " " AIDS (Budget, Budget) = for Time: 30*60% = 18 "" Time " " for Newsweek: 30*40% = 12 " " Budget (30, 70*) (18, 12) " " " " " " " " " --> Here Newsweek doesnt have a dominant strategy, but Time does because it was Newsweeks payoffs " Newsweek would them foresee that that cause its payoffs for AIDS stop being unifor-" " Time has a dominant strategy of AIDS, mly higher than those of Budget as a strategy, as a " which means that it will surely choose result of the supposition of a preference. And there "" this option. Therefore, the outcome of is also a dominated strategy for Time, which " " the game is (AIDS, Budget) and the is Budget, since it yields the magazine a uniformly " " respective payoffs (70, 30). lower payoff, regardless of what Newsweek does.