Environmental Engineering Reference
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UA
-180, 150
0, -20
t
D (0.5)
~D (0.5)
RA
-200, 150
R.1
~t
M.1
-40, 80
-170, -40
t
D (0.5)
~D (0.5)
~A
-210, 150
M.2
~t
-30, 0
Figure 10.14
The trespassing game with two players and numerical values
Ep (RA/~t) 5 −40 . Ep (UA) 5 −180 . Ep (~A/t)
5 −170(0.5) -210(0.5) 5 −85 -105 5 −190
Note that if the state decided to completely restrict access (~A) the best
response strategy for the community would be to trespass (t), the payof s
for these strategies being (−190, 55), yielding a negative joint payof of
-135.
Given the rules, available strategies and values for this game, the result
will be to regulate access and not to trespass (RA, ~t) illustrated by a
square. Note that from the way in which the payof s were given, the result-
ing pair of strategies is also the one that yields the higher social proi ts, since
the joint proi ts of regulating access and not trespassing (RA,~t) are equal
to 40, being the highest joint proi t that can be achieved in this game.
Notes
1. Current applications of game theory include biology, engineering, political science,
internal relations, computer science and philosophy.
2.
In economic jargon, the payof s represent utilities that comply with the Von Neumann-
Morgenstern axiom.
3.
If there are subsequent nodes involving probabilities, starting with the payof s at the
terminal nodes, we would move from right to left computing the conditional or inde-
pendent probabilities, following the rules for independent or conditional probabilities
respectively.
4.
In some cases knowing that one outcome is preferred over another is enough to derive
a preferred strategy.
5.
A pair of strategies with these properties is called a Nash equilibrium, after J. Nash
(1953) who showed that all games with a i nite number of strategies have at least
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