OVERVIEW OF GAME THEORY

1.         What is Game Theory?

It is part of the theory of purposeful behavior commonly known as “rational choice theory”

It specifically focuses on situations with two or more interdependent decision makers

The name “game theory” may be unfortunate, as it suggests frivolity

It might better be called the conceptual analysis of

            interdependent decision or

            conflict and cooperation or

            strategy and coalitions

In any case the “games” referred are not:

            games of physical or mental skill

            games of pure chance

            “games people play”

The games referred to are games of strategy, i.e., “parlor games” such as

            board games (tic-tac-toe, checkers, chess)

            card games (bridge, poker)

Why do serious people go about trying to construct a “theory of [such] games”?

von Neumann & Morgenstern (below, p. 2):

The typical problems of economic [and many problems of social and political] behavior become strictly identical with the mathematical notions of suitable games of strategy.

2.         What are games of strategy (considered abstractly)?

Games of strategy, defined by a set of

            two or more players, and

            each player is assigned a set of possible strategies (or actions or moves or choices)

Each possible combination of strategies, one for each player, produces an outcome

Each player has preferences (or interests, values, etc.), more or less conflicting, over the possible outcomes

Game theory develops two important insights concerning such games

            Iin a board games (like chess) at least, once the “end game” (last few moves) is reached it becomes clear that one player has a “winning position” and the other player may as well resign, so we ask:

Is there (at least in principle) a best way to play that will guarantee victory (or a draw) from the very first move?

What general characteristics of games determine the answers to this question, i.e., determine their inherent logic?

3.         History of Game Theory

Early papers by Zermelo (1912, perfect information), Borel (1927, mixed strategies), von Neumann (1928, minimax theorem)

Von Neumann and Morgenstern, Theory of Games and Economic Behavior (1944)

General development of mathematical theory of games (at Fine Hall [Princeton Mathematics Department] and RAND Corporation), late 1940s onwards (especially work of John Nash on non-cooperative games and [Nash] equilibrium), with possible applications to Cold War nuclear strategy

Game theory was brought to attention of social scientists in mid-1950s (Luce and Raiffa, Games and Decisions, 1957)

Some political applications by non-political scientists at this time (Arrow, Social Choice and Individual Values (1951), Black, Theory of Committees and Elections (1958), Downs, An Economic Theory of Democracy (1957), Schelling, The Strategy of Conflict (1960), Buchanan & Tullock, The Calculus of Consent (1962)

Earliest work by a political scientist: Riker, The Theory of Political Coalitions (1962) followed by much further work by Riker and his students who constituted the “Rochester school” (late 1960s to early 1970s)

Game theory enters mainline political science (late-1970s)

Game theory (and “number crunching”) allegedly dominates mainstream political science, provoking the “Perestroika movement” within the discipline

Game theory publicized by A Beautiful Mind biography (and later movie) about John Nash