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to one kilometer in the first turn, the
second player then takes up to two
kilometers, the first player then gets
up to three kilometers, the second
then gets up to four kilometers, and
so on.
Warm-up. Suppose the line segment is five kilometers long from a
stake at kilometer 0 to a stake at kilometer 5. Suppose the first player
takes between 0 and 1 kilometer.
Which player would get more of the
line segment, assuming each plays
optimally?
Answer to warm-up. Player 2. Player
1 takes kilometer 0 to 1. Player 2 then
takes kilometers 2 to 4. The first play-
er then takes one of the two remain-
ing kilometers— 1 to 2 or 4 to 5—and
the second player then takes the oth-
er remaining kilometer. The second
player ends up with lease rights to
three of the
protocol, whereby each company
(player) takes turns to acquire non-
overlapping sections of a full seg-
ment. The first player may take up
THE VAST UNDERGROUND lava fields in
the western U.S. feature a photogenic
geyser called Old Faithful. Eruptions
send approximately 15,000 liters of
steaming water 50 meters into the
air approximately every hour. Unfortunately, what is underground is not
nearly as appealing. If the lava fields
erupted in a major way, they could
cause ferocious firestorms that would
destroy a large portion of the western
U.S. and Canada and substantially
cool the planet.
Now imagine a pair of tunnel-boring energy-extraction companies
are competing to cool the lava, make
some money, and provide carbon-free
energy besides. The idea is to tunnel
from a power plant outside the lava
fields to near the lava, but not too
close, to avoid accidental eruptions. A
pipeline could in theory then take cool
water from the power plant to the end
of the tunnel where the water would
be heated into steam and the steam
would power the turbines of the power
plant. The whole system could be designed to recycle the steam back into
water in a closed loop.
In this scenario, the federal government, which owns the land, steps
in to lease the energy rights, identifying cross-sections underground
to which tunnels can be drilled. The
government identifies those underground cross-sections based on
their more-or-less linear segments
aboveground, so leasing a segment
would confer the right to tap the lava
in the vertical cross-section below
that segment.
To encourage participation in
the project while achieving equity
for both companies, government
mathematicians design a game-style
Upstart Puzzles
Fighting for Lava
[CONTINUED ON P. 143]
DOI: 10.1145/3314071 Dennis Shasha
Imagine a pair
of tunnel-boring
energy-extraction
companies are
competing to cool
the lava, make some
money, and provide
carbon-free
energy besides.
“First player gets to claim up to
one kilometer, the second up to two, the
first up to three, and so on. Should I try to go
first or second in order to maximize
my access to the lava fields.”