Q. Explain the Game theory?
Game theory: Game theory is a branch of applied mathematics which is used in the social sciences, most particularly in economics, as well as in biology (specifically evolutionary biology and ecology), political science, engineering, international relations, computer science and philosophy. Game theory tries at mathematically capturing behaviour in strategic situations or games in that an individual's success in making choices relies on the choices of others. Whereas initially developed to analyse competitions in that one individual does better at another's expense (zero sum games), it has been expanded to treat a wide class of interactions, that are classified according to numerous criteria.
Today, "game theory is a sort of umbrella or 'unified field' theory for rational side of Social science, where 'social' is interpreted broadly, to include human as well as non-Human players (computers, animals, plants)" (Aumann 1987).
Traditional applications of game theory aim at finding equilibrium in these games. In equilibrium, every player of the game has adopted a strategy which they are unlikely to change. Many equilibrium concepts have been developed (most famously Nash equilibrium) in an endeavour to capture this idea. These equilibrium concepts are differently motivated contingent on the field of application, though they frequently coincide oroverlap. This methodology isn't without criticism and debates continue over the appropriateness of particular equilibrium concepts, appropriateness of equilibrium altogether and usefulness of mathematical models more commonly.
Though some developments took place before it, the field of game theory came into being with Émile Borel's researches in his 1938 book Applications aux Jeux des Hazard and was followed by the 1944 book Theory of Games and Economic Behaviour by John von Neumann and Oskar Morgenstern. This theory was developed extensively in 1950s by many scholars. Game theory was afterwards explicitly applied to biology in the 1970s, though similar developments go back at least as far as the 1930s. Game theory has been widely recognised as a significant tool in many fields. Eight game theorists have won the Nobel Memorial Prize in Economic Sciences and John Maynard Smith was awarded the Crafoord Prize for his application of game theory to biology.
The games studied in game theory are well-defined mathematical objects. A game consists of a set of players, a set of moves (or strategies) available to those players and a specification of payoffs for each combination of strategies. Most cooperative games are presented in the characteristic function form, while the extensive and the normal forms are used to define non-cooperative games.