Game theory
is a branch of applied mathematics that is often used in the context of
economics. It studies strategic interactions between agents. In strategic games, agents choose
strategies that will maximize their return, given the strategies the other agents choose. The
essential feature is that it provides a formal modeling approach to social situations in which
decision makers interact with other agents. Game theory extends the simpler optimization
approach developed in neoclassical economics.
The normal (or strategic form)
game is usually represented by a matrix which shows the
players, strategies, and payoffs (see the example to the right). More generally it can be
represented by any function that associates a payoff for each player with every possible
combination of actions.
When a game is presented in normal form, it is presumed that each player acts simultaneously
or, at least, without knowing the actions of the other. If players have some information about
the choices of other players, the game is usually presented in extensive form.
In game theory, the Nash equilibrium
is a solution concept of a game involving two or
more players, in which no player has anything to gain by changing only his or her own
strategy unilaterally. If each player has chosen a strategy and no player can benefit by
changing his or her strategy while the other players keep theirs unchanged, then the current
set of strategy choices and the corresponding payoffs constitute a Nash equilibrium.
Stated simply, A and B are in Nash equilibrium if A is making the best decision A can, taking
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 h
 Game Theory, Nash

Click to edit the document details