Environmental Engineering Reference
In-Depth Information
row). Thus, the dominant strategy for player 2 will also be to settle. The
horizontal arrows represent the best response strategies for player 2.
When a game has at least one of a player's arrows pointing to a box and
at least an arrow of the other player pointing to the same box, then the
pair of strategies is said to be in a Nash equilibrium.
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A Nash equilibrium
is thus dei ned as any pair of strategies with the property that each player
maximizes her or his payof given the actions of the other player. In this
case, the Nash equilibrium for this game is settle/settle.
There are additional names for specii c strategies and equilibria. A pure
strategy is one that does not involve chance (probabilities). And a pure
Nash equilibrium is the equilibrium reached when each player plays a pure
strategy. In the game illustrated in Figure 10.3, there is only one Nash
equilibrium (S,S) and this is a pure Nash equilibrium, since it does not
involve probabilities. Another type of strategy, not present in this game, is
mixed strategies. A mixed strategy requires a player to randomize her or
his pure strategies in order to keep the opponent guessing. Consequently,
a mixed equilibrium is the equilibrium reached when each of the players is
playing a mixed strategy.
Two further equilibrium notations are used for specii c purposes in
game theory. Symmetric equilibrium, in which every player chooses the
same strategy and an asymmetric equilibrium in which at least two players
choose dif erent strategies. When there is only one equilibrium in the
game, this is called the unique Nash equilibrium and when there is more
than one equilibrium, it is said that the game has multiple Nash equilibria.
In the game presented in Figure 10.3, there is a unique pure symmetric
Nash equilibrium. This equilibrium is represented with a star in the middle
(note the star in the middle of the box settle/settle), though there are many
other identii able forms for illustrating where the Nash equilibria are.
Having presented a brief review of game-theoretic language and repre-
sentation forms, next section will review the game-theoretic approach to
CPRs.
Game theory, common pool resources (CPRs) and common pool
institutions (CPIs)
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Game theory has been extensively used as a framework for analysis of
CPR problems (see Ostrom et al., 1994; Baland and Platteau, 1996).
Before presenting the game-theoretic approach to common pool resources
(CPRs), it is important to review the way CPRs have been conceived and
the problems arising in the management of these resources.
Common pool resources have been mainly explained in terms of the phys-
ical attributes of the goods or resources. CPRs are considered to share two
characteristics: (1) the dii culty of excluding individuals from benei ting
