Environmental Engineering Reference
In-Depth Information
Rain (
)
X
1
Settle
N.1
Drought (1 -
)
X
2
Pastoralist.1
Rain (
)
X
3
Migrate
N.2
Drought (1 -
)
X
4
Source:
After Bardhan (1993).
Figure 10.1
Example of an extensive form game
Non-cooperative extensive form games
Non-cooperative games can be depicted in two forms: extensive and
strategic forms. In the extensive form, the rules of the game are laid out
in full detail by drawing a tree (Figure 10.1). To illustrate the way in
which extensive games are constructed, consider a simplii ed decision
problem faced by an agro-pastoralist. He or she can decide whether to
settle in an area of land, or to migrate. Her or his decision will depend on,
among other things, the rainfall patterns she or he expects to encounter
in dif erent places. Consider then the following game tree (extensive form
game) with two players (player 1 and player 2). Player 1 will represent the
agro-pastoralist (P) and player 2 will represent nature (N).
Pastoralist.1 represents the node at the root of the tree from which the
i rst available strategies follow. The strategies are named branch lines in
this representation form, and depart from the small circles called nodes.
In this game, the two available strategies for the agro-pastoralist are to
settle in the current land or to migrate and move to another place. The
next nodes of the game N.1 and N.2 represent two dif erent nodes for
nature. When two nodes are connected with a dotted line, which is not the
case in this example, it is said that both nodes are in the same information
set. That is, there is incomplete information about the actions of the last
player. Otherwise, as we move forward in the tree from left to right, infor-
mation about the last player's moves is gained along the way.
In this game, the two available strategies for nature are rain or
drought. In reality the level of rainfall could fall at dif erent levels along
