Environmental Engineering Reference
In-Depth Information
Game theory; language and representation forms
Game theory is a mathematical theory used to understand the outcomes
of strategic interactions in terms of quantii able gains and losses from
dif erent decisions, to mostly competing players, as if they were playing a
game. As a branch of applied mathematics, game theory started to be used
as a framework for analysis after the publication of Von Neumann and
Morgenstern's (1944)
Theory of Games and Economic Behavior
. As such,
the main use of game theory was in economics through the early 1970s,
when its use started to spread to other sciences.
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There are two major strands within game theory: cooperative and non-
cooperative game theory. Cooperative game theory deals with situations
in which the players can negotiate before the game is played on what to
do in the game. It is assumed that these negotiations result in signing
a binding agreement (Binmore, 1994). For this type of game, what is
important is not so much the strategies available to the players, but the
preference structure of the game itself, since this is what determines which
contracts are feasible.
Non-cooperative game theory is based on a dif erent set of principles.
Non-cooperative game theory calls for a complete description of the rules
of a game so that the strategies available to the players can be studied in
detail. The objective is to i nd a pair of equilibrium strategies to be des-
ignated as the solution of the game and this solution might or might not
be cooperative (Binmore, 1994). This strand of game theory gives space
to agreements. However, these are not conceived as necessarily binding.
Agreements can be made after or before a game is played and, depending
on how the payof s and strategies available change, agreements can or
cannot be sustained.
At this stage, it is important to point out that game theory is not the
same as game models (Snidal, 1985). Game theory sets out an analytical
framework for the construction of game models, not for their design.
The results of the game will change depending on the way the model is
conceived. This means that one could construct a model and give dif er-
ent features, for example, increase the number of players, and the result
would be dif erent. Game theory thus can be conceived as a 'metalan-
guage for [the construction of] game-theoretic models' (Ostrom et al.,
1994, p. 24).
As most of the games used for depicting CPR problems emanate
from non-cooperative game theory, the next section intends to outline
some of the key concepts used in non-cooperative game theory to familiar-
ize the reader with game-theoretic language and forms of representation.
