Environmental Engineering Reference
In-Depth Information
Solving for the past inequality, b would have to be higher than 2/6 for set-
tling to be the preferred strategy for the agro-pastoralist. This means that
for all probabilities of rain higher than 0.33 it will always be best for the
agro-pastoralist to settle.
Clearly this is a simplii ed view of the available decisions to the agro-
pastoralist and of the variables that will shape his or her payof s. However,
once familiar with the way games can be constructed and solved, and the
interactions amongst several players, games illustrating real-life situations
can be constructed. The next section will introduce the other, usually more
often used, form of game in non-cooperative game theory, the 'normal' or
strategic form game.
Non-cooperative strategic form games
The other form in which non-cooperative games are depicted is the normal
or strategic form (Figure 10.3). This form is useful to depict interactions
amongst two or more players in which their payof s are shaped on what
the other player does and for illustrating simultaneous decision-making.
Consider two agro-pastoralists or two groups of agro-pastoralists:
agro-pastoralist 1 (player 1) and agro-pastoralist 2 (player 2). In normal/
strategic form games, the payof s for each of the players are depicted
within the boxes of the matrix (Figure 10.3). In some normal form repre-
sentations, the payof s are written in a parenthesis with the i rst number
being the player 1 payof and the second number or letter in the parenthe-
sis, the player 2 payof . In other normal form representations, for example
the game in Figure 10.3, the payof s are depicted at the corners of each
Past.2
Settle
Migrate
0.75
1.5
Settle
*
0.75
0.5
Past.1
0.5
-1
Migrate
1.5
-1
Source:
After Bardhan (1993).
Figure 10.3
A normal 2 × 2 form of the revisited 'migration game'
