The study of the theory of games was started in Von Neumann (1928), but
the development of the theory of games was accelerated after the
publication of the classical book "Theory of games and economic
behavior" by Von Neumann and Morgenstern (1944). As an initial step, the
theory of games aims to put situations of conflict and cooperation into
mathematical models. In the second and final step, the resulting models
are analysed on the basis of equitable and mathematical reasonings. The
conflict and/or cooperative situation in question is generally due to
the interaction between two or more individuals (players). Their
interaction may lead up to several potential payoffs over which each
player has his own preferences. Any player attempts to achieve his
largest possible payoff, but the other players may also exert their
influence on the realization of some potential payoff. As already
mentioned, the theory of games consists of two parts, a modelling part
and a solution part. Concerning the modelling part, the mathematical
models of conflict and cooperative situations are described. The
description of the models includes the rules, the strategy space of any
player, potential payoffs to the players, the preferences of each player
over the set of all potential payoffs, etc. According to the rules, it
is either permitted or forbidden that the players communicate with one
another in order to make binding agreements regarding their mutual
actions.
