# Supplement 2 Model of flood-related losses. ```Supplement 2 Model of flood-related losses.
A simple model for flood-related losses from fish farms was constructed based on empirical survey
findings. The model greatly simplifies reality by treating stocking level or density as a proxy variable
for level of investment, and thus the riskiness of a cropping decision. The model was used to derive a
pay-off matrix that could be into a fish farming simulation game. The assumptions of the flood risk
model will now be described.
Value of harvest (Hd) at stocking density d is assumed to be directly proportional to, and double, the
input costs (Cd):
Hd = 2Cd
In this system variable costs (for stock, feed, medication and labor or labor-opportunity) dominate
costs and fixed costs (equipment or cages) have short life spans, so fixed costs were assumed to be
zero or subsumed within variable costs.
Profit from a crop (Pd) if no flood (f=0) is then just equal to input cost or
Pd,0 = Cd if f = 0
Profits from a crop if a flood (f=1) occurs is adjusted for reduced value of harvest (1-Ld) and nonharvest related loss (k), for example, to cages or equipment, assumed to be proportional to cost:
Pd,1 = 2 Cd (1-Ld) – k Cd if f=1
The fraction of harvest lost for flood was set at following values for three stocking densities (low,
medium, high): Llo=0.15, Lmd=0.65, Lhi=1. The non-harvested costs was set at constant k = 1.7.
The expected pay-offs for probability of flood α are then:
E(Pd) = α Pd,1 + (1-α) Pd,0
The pay-off matrix for this model was calculated using above assumptions and is shown in the table
in Figure 2 in the main text along with the expected pay-offs for each fixed stocking strategy across a
range of flood probabilities.
The values used in the actual game were derived from the standardized matrix where high stock, no
flood, has a value of 1 by multiplying all entries by 100 – interpreted with farmers in units of a
thousand Baht. The average expected payoff in this game with random strategies for range of
probabilities from 0.1 to 0.5 is 19 (thousand) close to the observed median profit for a last harvested
crop of 20 (thousand) baht.
```