Environmental Engineering Reference
In-Depth Information
box within the matrix, the payof to the left top corner of the box being
the payof for player 1 (agro-pastoralist 1) and the one located at the right
bottom of the box, being the payof for player 2 (agro-pastoralist 2). One
of the players plays the columns and the other player plays the rows. The
names of the players and available strategies are written at the top of the
columns and at the side of the rows, respectively.
Drawing on the example presented in the past section, suppose that the
payof s for the agro-pastoralists are not only dependent on what she or
he thinks nature will do, but on what other agro-pastoralists do. Suppose
then that the payof s from settling for the agro-pastoralist will be shaped
by what other agro-pastoralists do and vice versa. For example, if land
is scarce then if both agro-pastoralists settle in the same area the benei ts
for each agro-pastoralist will be reduced. If both agro-pastoralists decide
to settle in the area (settle, settle), the payof for each agro-pastoralist will
no longer be 1.5 as derived in the past example. If both agro-pastoralists
decide to stay, each will only receive 0.75. If only one of them decides to
migrate, the one who settles will receive 1.5 while the one who migrates will
receive 0.5. If, on the other hand both players decide to migrate, each of
them will receive -1. That is, both players would carry the costs and risks
of migrating and the fact that both will graze in the same area imposes a
burden on one another.
In order to derive the contingent or best response strategies for each
player given the payof s for the game and what the other player does, let
us start with player 1. What would the best response for agro-pastoralist
1 be if she or he thinks agro-pastoralist 2 will settle (left column)? Given
that strategy by player 2, the best response strategy for player 1 is to settle
since 0.75 . 0.5 (the two payof s at the left top corner of the two boxes in
the left column). If, on the other hand, agro-pastoralist 2 migrates (right
column), the best response for agro-pastoralist 1 would be to settle since
1.5 . −1. These best response strategies are illustrated by arrows at the
sides of the matrix. The vertical arrows illustrate agro-pastoralist 1's best
response strategies for this game. In this game, player 1 (agro-pastoralist
1) has a dominant strategy. A dominant strategy is a strategy that given
the rules and payof s of the game, in any specii c node, is preferred by a
player no matter what the other player does.
The procedure followed with player 1 now needs to be done with player
2. What would the preferred strategy for player 2 be, given the actions
of the other player? If player 1 decides to settle (top row), player 2's best
response strategy would be to settle given that 0.75 . 0.5 (bottom right
payof s from boxes in the top row). If, on the other hand, player 1 decides
to migrate (bottom row), the best response strategy for player 2 will still
be to settle, since 1.5 . −1 (bottom right payof s from boxes in the bottom
