Environmental Engineering Reference
In-Depth Information
C
10,10
C
-1,11
D
1
2
C
11,-1
D
D
0,0
Source:
Dawes (1973).
Figure 10.7
Adaptation of the prisoner's dilemma game in extensive form
and numerical payof s
Now, consider that this game is not i nite. That is, there is not only one
round to the game, but that the game is played over and over again. This
leads to the alternative game set by Ostrom (1990) following the structure
of the prisoner's dilemma game but adding two branches for each player
at the beginning of the game. These branches are termed: agree (A) or do
not agree (~A). That is, players can get together and arrange a contract in
order to arrive at a joint payof (Figure 10.8).
In this game, the issues are: (1) whether the contracts can be binding,
that is, there is unfailing enforcement and (2) whether the payof s are such
that the transaction costs of enforcing the contract are lower than the
expected gains from the contract. A binding contract is interpreted in non-
cooperative game theory as one that is unfailingly enforced by an external
actor. The cost of enforcing the agreement is denoted in Figure 10.8 by
e
.
Given the payof s and structure of the game, the dominant equilibrium
is having both parties agreeing to cooperate. The equilibrium is shown
in the rectangle at the bottom of the tree. If these strategies are followed,
players will receive the joint benei t from cooperation minus the shared
enforcement costs (10 -
e
/20, 10 −
e
/20). Note that this equilibrium will
hold only if joint enforcement costs (
e
) are lower than 20.
Encouraged by this and other parallel work, over the past few decades
theorists have explored the relationships between rules, institutions,
property rights and resource user characteristics for arriving at coopera-
tive outcomes that can enhance collective benei ts. The next section will
illustrate the use of game theory for identifying key variables and levels of
