Environmental Engineering Reference
In-Depth Information
Rain (0.5)
6
Settle
N.1
Drought (0.5
)
-3
Pastoralist.1
Rain (0.5)
2
Migrate
N.2
Drought (0.5
)
-1
Source:
After Bardhan (1993).
Figure 10.2
The 'migration game' with numerical payof s
Ep
(
S
) 5 6(0.5) 2 3(0.5) 5 3 2 1.5 5 1.5
Conversely, the expected payof from migrating would be:
Ep
(
M
) 5 2(0.5) 2 1(0.5) 5 1 2 0 .5 5 0.5
Given these payof s and probabilities, the best strategy for the agro-
pastoralist would be to settle since the expected payof from settling will be
higher than the expected payof from moving (
Ep
(
S
) .
Ep
(
M
)). An arrow
on the 'settle' branch denotes this.
Now, let us consider another approach to this game. What if the agro-
pastoralist is not sure about the probabilities of drought or rain? How
much would the expected probability have to fall or rise in order for
the chosen strategy to still be preferred? To i nd a solution, we need to
compute the same expected payof s and solve for b:
Ep
(
S
) 5 6b 2 3(1 2 b) 5 9b 2 3
And,
Ep
(
M
) 5 2b 2 1(1 2 b) 5 3b 2 1
For settling to be a preferred strategy,
Ep
(
S
) .
Ep
(
M
), thus:
9b 2 3 . 3b 2 1
