Economic and Game Theory What is Game Theory?

[Open Book]      by David K. Levine, Department of Economics, UCLA

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An Instructive Example | Learn More About Game Theory

What economists call game theory psychologists call the theory of social
situations, which is an accurate description of what game theory is about.
Although game theory is relevant to parlor games such as poker or bridge,
most research in game theory focuses on how groups of people interact. There
are two main branches of game theory: cooperative and noncooperative game
theory. Noncooperative game theory deals largely with how intelligent
individuals interact with one another in an effort to achieve their own
goals. That is the branch of game theory I will discuss here.

In addition to game theory, economic theory has three other main branches:
decision theory, general equilibrium theory and mechanism design theory. All
are closely connected to game theory.

Decision theory can be viewed as a theory of one person games, or a game of
a single player against nature. The focus is on preferences and the
formation of beliefs. The most widely used form of decision theory argues
that preferences among risky alternatives can be described by the
maximization the expected value of a numerical utility function, where
utility may depend on a number of things, but in situations of interest to
economists often depends on money income. Probability theory is heavily used
in order to represent the uncertainty of outcomes, and Bayes Law is
frequently used to model the way in which new information is used to revise
beliefs. Decision theory is often used in the form of decision analysis,
which shows how best to acquire information before making a decision.

General equilibrium theory can be viewed as a specialized branch of game
theory that deals with trade and production, and typically with a relatively
large number of individual consumers and producers. It is widely used in the
macroeconomic analysis of broad based economic policies such as monetary or
tax policy, in finance to analyze stock markets, to study interest and
exchange rates and other prices. In recent years, political economy has
emerged as a combination of general equilibrium theory and game theory in
which the private sector of the economy is modeled by general equilibrium
theory, while voting behavior and the incentive of governments is analyzed
using game theory. Issues studied include tax policy, trade policy, and the
role of international trade agreements such as the European Union.

Mechanism design theory differs from game theory in that game theory takes
the rules of the game as given, while mechanism design theory asks about the
consequences of different types of rules. Naturally this relies heavily on
game theory. Questions addressed by mechanism design theory include the
design of compensation and wage agreements that effectively spread risk
while maintaining incentives, and the design of auctions to maximize
revenue, or achieve other goals.

An Instructive Example

One way to describe a game is by listing the players (or individuals)
participating in the game, and for each player, listing the alternative
choices (called actions or strategies) available to that player. In the case
of a two-player game, the actions of the first player form the rows, and the
actions of the second player the columns, of a matrix. The entries in the
matrix are two numbers representing the utility or payoff to the first and
second player respectively. A very famous game is the Prisoner's Dilemma
game. In this game the two players are partners in a crime who have been
captured by the police. Each suspect is placed in a separate cell, and
offered the opportunity to confess to the crime. The game can be represented
by the following matrix of payoffs

            not        confess
            confess
 not
 confess    5,5        0,10
 confess    10,0       1,1

Note that higher numbers are better (more utility). If neither suspect
confesses, they go free, and split the proceeds of their crime which we
represent by 5 units of utility for each suspect. However, if one prisoner
confesses and the other does not, the prisoner who confesses testifies
against the other in exchange for going free and gets the entire 10 units of
utility, while the prisoner who did not confess goes to prison and gets
nothing. If both prisoners confess, then both are given a reduced term, but
both are convicted, which we represent by giving each 1 unit of utility:
better than having the other prisoner confess, but not so good as going
free.

This game has fascinated game theorists for a variety of reasons. First, it
is a simple representation of a variety of important situations. For
example, instead of confess/not confess we could label the strategies
"contribute to the common good" or "behave selfishly." This captures a
variety of situations economists describe as public goods problems. An
example is the construction of a bridge. It is best for everyone if the
bridge is built, but best for each individual if someone else builds the
bridge. This is sometimes refered to in economics as an externality.
Similarly this game could describe the alternative of two firms competing in
the same market, and instead of confess/not confess we could label the
strategies "set a high price" and "set a low price." Naturally is is best
for both firms if they both set high prices, but best for each individual
firm to set a low price while the opposition sets a high price.

A second feature of this game, is that it is self-evident how an intelligent
individual should behave. No matter what a suspect believes his partner is
going to do, is is always best to confess. If the partner in the other cell
is not confessing, it is possible to get 10 instead of 5. If the partner in
the other cell is confessing, it is possible to get 1 instead of 0. Yet the
pursuit of individually sensible behavior results in each player getting
only 1 unit of utility, much less than the 5 units each that they would get
if neither confessed. This conflict between the pursuit of individual goals
and the common good is at the heart of many game theoretic problems.

A third feature of this game is that it changes in a very significant way if
the game is repeated, or if the players will interact with each other again
in the future. Suppose for example that after this game is over, and the
suspects either are freed or are released from jail they will commit another
crime and the game will be played again. In this case in the first period
the suspects may reason that they should not confess because if they do not
their partner will not confess in the second game. Strictly speaking, this
conclusion is not valid, since in the second game both suspects will confess
no matter what happened in the first game. However, repetition opens up the
possibility of being rewarded or punished in the future for current
behavior, and game theorists have provided a number of theories to explain
the obvious intuition that if the game is repeated often enough, the
suspects ought to cooperate.

If you wish to learn more about game theory, there a variety of good books
on the topic.

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© David K. Levine.

 What is Game Theory?