

game
A game is a model with (1) players who make (2) strategy (or action) choices in a (3) predefined time order, and then (4) receive payoffs, which are usually conceived of in money or utility terms. Classic games are the Prisoner's Dilemma, Matching Pennies, the Battle of the Sexes, the dictator game, the ultimatum game, the Bertrand game, and the Cournot game.

game theory
game theory

Game theory
Theory of rational behavior for interactive decision problems. In a game, several
agents strive to maximize their (expected) utility index by chosing
particular courses of action, and each agent's final utility payoffs depend on the profile of
courses of action chosen by all agents.
The interactive situation, specified by the set of participants, the possible courses of action
of each agent, and the set of all possible utility payoffs, is called a game; the agents
'playing' a game are called the players.
In denegerate games, the players' payoffs only depend on their own actions. For example,
in competitive markets (competitive market equilibrium), it is enough that each
player optimizes regardless of the behavior of other traders. As soon as a small number of
agents is involved in an economic transaction, however, the payoffs to each of them depend on
the other agents' actions. For example in an oligopolistic industry or in a cartel, the price or the
quantity set optimally by each firm depends crucially on the prices or quantities set by the
competing firms. Similarly, in a market with a small number of traders, the equilibrium price
depends on each trader's own actions as well as the one of his fellow traders (see auctions).
Whenever an optimizing agent expects a reaction from other agents to his own actions,
his payoff is determined by other player's actions as well, and he is playing a game.
Game theory provides general methods of dealing with interactive optimization problems; its
methods and concepts, particularly the notion of strategy and strategic
equilibrium find a vast number of applications throughout social sciences (including
biology). Although the word 'game' suggests peaceful and 'kind' behavior, most situations revelant
in politics, psychology, biology, and economics involve rather strong conflicts of interest, competition,
and cheating, apart from leaving room for cooperation or mutually benefically actions.
Based on a model of optimizing agents that plan individually optimal course of play, knowing
that her opponents will do so as well, the basic objects of interest in strategic (or 'noncooperative')
game theory are the players' strategies. A player's strategy is a complete plan of
actions to be taken when the game is actually played; it must be completely specified before the
actual play of the game starts, and it prescribe the course of play for each decision that a
player might be called upon to take, for each possible piece of information that the player may have
at each time where he might be called upon to act.
A strategy may also include random moves. It is generally assumed that the players
evaluate uncertain payoffs according to von Neumann Morgenstern
utility.
In addition to the strategic branch of game theory, there is another one that focuses on the
interactions of groups of players that jointly strive to maximize their surplus. While this
second branch represents the analysis of coalitional games, which centers around notions
of 'coalitionally stable' payoff configurations, we focus here on strategic game theory (from which
coalitional games are derived).
Given a strategic game, a profile of strategies results in a profile of (expected) utility payoffs.
A certain payoff allocation, or a profile of final moves of the players is called an outcome
of the game. An outcome is called an equilibrium outcome if no player can unilaterally
improve the outcome (in terms of his own payoff) given that the other players stick to their
equilibrium strategies.
A profile of strategies is called a (strategic) equilibrium if, given that all players
conform to the prescribed strategies, no player can gain from unilaterally switching to another
strategy. Alternatively, a profile of strategies forms an equilibrium if the strategies form best
responses to one another.
(Unfortunately, it is impossible to describe what is an equilibrium other than in such a
selfreferential way. The best way to understand this definition is then to take it literally.)
Only equilibrium outcomes are reasonable outcomes for games, because outside an equilibrium
there is at least one player that can improve by playing according to another strategy.
An implicit assumption of game theory is that the players, being rational, are able to
reproduce any equilibrium calculations of anybody else. In particular, all the equilibrium
strategies must be known to (as they are computed by) the players. Similarly, it is assumed
that the whole structure of the game, in much the same way as the players' social context, is
known by each player (and that this knowledge itself is known etc.)

Game tree
Time structure of possible moves describing an extensive form game. A game tree is a set of
nodes some which are linked by edges. A tree is a connected graph with no cycles. The first move
of the game is identified with a distinguished node that is called the root of the tree. A play of the
game consists of a connected chain of edges starting at the root of the tree and ending, if the game
is finite, at a terminal node. The nodes in the tree represent the possible moves in the game. The
edges leading away from a node represent the choices or actions available at that move. Each
node other than the terminal node is assigned a player's name so that it is known who makes the
choice at that move. Each terminal node must be labeled with the consequences for each player
if the game ends in the outcome corresponding to that terminal node.

gamma (of options)
As used with respect to options: The rate of change of the portfolio's delta with respect to the price of the underlying asset. Formally this is a partial derivative.
A portfolio is gammaneutral if it has zero gamma.

gamma distribution
A distribution relevant to, for example, waiting times. Expression of its pdf requires reference to the gamma function which will be called GAMMA(a) here. (When HTML supports math a better display will be possible.) The gamma distribution's pdf has parameters a>0 and b>0, and GAMMA(a) is also greater than zero. The support is on x>0: f(x)=[x^{a1}e^{x/b}]/[GAMMA(a)b^{a}]

gamma function
A function of a real a>0. It is the integral over y from zero to infinity of y^{a1}e^{y} dy. This integral is the gamma function of a, GAMMA(a). (When HTML supports math a better display will be possible.) The gamma distribution is a function that includes the gamma function.

GARCH
Generalized ARCH. First paper may have been Bollerslev, 1986, Journal of Econometrics

GARP
abbreviation for the Generalized Axioms of Revealed Preference.

Gauss
A matrix programming language and programming environment. Made by Aptech.

Gaussian
an adjective that describes a random variable, meaning it has a normal distribution.

Gaussian kernel
The Gaussian kernel is this function: (2PI)^{.5}exp(u^{2}/2). Here u=(xx_{i})/h, where h is the window width and x_{i} are the values of the independent variable in the data, and x is the value of the independent variable for which one seeks an estimate. Unlike most kernel functions this one is unbounded on x; so every data point will be brought into every estimate in theory, although outside three standard deviations they make hardly any difference. For kernel estimation.

Gaussian white noise process
A white noise process with a normal distribution.

GDP
Gross domestic product. For a region, the GDP is "the market value of all the goods and services producted by labor and property located in" the region, usually a country. It equals GNP minus the net inflow of labor and property incomes from broad.  Survey of Current Business
A key example helps. A Japaneseowned automobile factory in the US counts in US GDP but in Japanese GNP.

GDP deflator
A measure of the cost of goods purchased by U.S. households, government, and industry. Differs conceptually from the CPI measure of inflation, but not by much in practice.

GEB
An abbreviation for the journal Games and Economic Behavior.

general equilibrium
general equilibrium

generalized linear model
A model of the form y=g(b'x) where y is a vector of dependent variables, x is a column vector of independent variables, b' is a row vector of parameters (that is, b is not a function of x) and g() is a possibly random function called a link function.
Examples: linear regression (y=b'x+errs) and logistic regression y=1/(1+e^{x})+errs.
An example that is not in the class of generalized linear models is: y=x_{1}*x_{2}.

Generalized Method of Moments
See GMM.

generalized Tobit
Synonym for Heckit.

generalized Wiener process
A continuoustime random walk with a drift and random jumps at every point in time (roughly speaking). Algebraically: a(x,t)dt + b(x,t)c(dt)^{.5} describes a generalized Wiener process, where: a and b are deterministic functions t is a continuous index for time x is a set of exogenous variables that may change with time dt is a differential in time c is a random draw from a standard normal distribution at each instant

generalized Wiener process

generator function
in a dynamical system, the generator function maps the old state N_{t} into new state N_{t+1} E.g. N_{t+1} = F(N_{t}). A steady state would be an N^{*} such that F(N^{*}) = N^{*}.

geometric mean
Geometric mean is a kind of average of a set of numbers that is different from the arithmetic average. The geometric mean is well defined only for sets of positive real numbers. Geometric mean of A and B is the square root of (A*B). The geometric mean of A, B, and C is the cube root of (A*B*C). And so forth. Contrast this to the arithmetic means, which are .5*(A+B) and .333*(A+B+C).

GEV
abbrevation for Generalized Extreme Value distribution. The difference between two draws of GEV type 1 variables has a logistic distribution, which is why a GEV distribution for errors gets assumed in certain binary econometric models.

GGH preferences
Refers to a paper by Greenwood, Hercowitz, and Huffman (1988) with utility functions across agents and across time by: u(C_{it}, N_{it}) = C_{it}  N_{it}^{b} where a>0 and b>1 are constants, and C_{it} and N_{it} stand for consumption and hours worked by each agent i at date t.  this utility function has Gorman form and so it aggregates  it has been successful at matching crosssection data relative to other functions that do.

Gibbs sampler
A way to generate empirical distributions of two variables from a model. Say the model defines probability distributions F(XY) and G(YX). Then start with a random set of possible X's, draw Y's from G(), then use those Y's to draw X's, and so on indefinitely. Keep track of the X's and Y's seen, and this will give samples enough to find the unconditional distributions of X and Y.

Gibrat's law
A descriptive relationship between size and growth  that the size of units and their growth percentage statistics are statistically independent. Sometimes Gibrat's law is thought to apply to large firms, and sometimes to cities (Gabaix, May 1999 American Economic Review, page 130).

Gini coefficient
A number between zero and one that is a measure of inequality. An example is the concentration of suppliers in a market or industry.
The Gini coefficient is the ratio of the area under the Lorenz curve to the area under the diagonal on a graph of the Lorenz curve, which is 5000 if both axes have percentage units. The meaning of the Gini coefficient: if the suppliers in a market have nearequal market share, the Gini coefficient is near zero. If most of the suppliers have very low market share but there exist one or a few supplies providing most of the market share then the Gini coefficient is near one.,
In labor economics, inequality of the wage distribution can be discussed in terms of a Gini coefficient, where the wages of subgroups are fractions of the total wage bill.

GlassSteagall Act
A 1933 United States national law separating investment banking and commercial banking firms. Also prohibited banks from owning corporate stock. It was designed to confront the problem that banks in the Great Depression collapsed because they held a lot of stock.

GLS
Generalized Least Squares. A generalization of the OLS procedure to make an efficient linear regression estimate of a parameter from a sample in which the disturbances are heteroskedastic. That is, in y = Xb + e (equation 1) that the e's vary in magnitude with the X's. The estimator of b is: (X'O^{1}X)^{1}X'O^{1}y (equation 2) where O, standing for omega, is the covariance matrix. (As you see in the estimator, the covariance matrix is assumed to be invertible.) The procedure to derive this is to multiply through the first equation by the square root of the inverse of the covariance matrix (which assumed to be known; if it estimated, one calls this procedure FGLS, for feasible GLS.) Then take OLS of the resulting equation.

GMM
Stands for Generalized Method of Moments, an econometric framework of Hansen, 1982. It is an approach to estimating parameters in an economic model from data. Used often to figure out what standard errors on parameter estimates should be.

GNP
Gross national product. The GDP is "the market value of all the goods and services producted by labor and property belonging to the region, usually a country. It equals GDP plus the net inflow of labor and property incomes from broad. A Japaneseowned automobile factory in the US counts in US GDP but in Japanese GNP.

Golden Rule capital rate
f'(k^{*})=(1+n) where k^{*} is optimal capital stock, f() is the aggregate production function, and n is population growth rate. f(k)k is consumed by the population. 'Golden Rule' may refer to a Solow fairy tale.

good
A good is a desired commodity.

goodwill
The accounting term to describe the premium that acquiring companies pay over the book value of the firm being acquired. Goodwill can include value for R&D and trademarks.

Gordon model
Of a stock price. From M. R. Gordon (1962). This model is sometimes used as a baseline for comparison or for intuition. Assume a constant rate of return r, and a constant dividend growth rate g. Define P_{t} to be the price of the stock in period t, and D_{t} to be its dividend in period t. Implication is that price of stock P_{t} = D_{t}/(rg).

Gorman form
A utility function or indirect utility function is in Gorman form if it is affine with respect to some argument. Which argument should be clear from context. E.g.: U_{i}(x_{i}, z) = A(z)x_{i} + B_{i}(z) Here the utility U_{i} for individual i is is affine in argument x_{i}. A critical implication is that the sum of Gorman form utility functions for individuals is a welldefined aggregate utility function under some conditions....

government failure
A situation, usually discussed in a model not in the real world, in which the behavior of optimizing agents in a market with a government would not produce a Pareto optimal allocation. The point is not that a particular government had, or would have, failed at something, but that the problem abstractly put cannot be perfectly solved by the government. The most common source of government failures in models is private information among the agents.

Granger causality
Informally, if one time series helps predict another, we can say it Granger causes the other. The original definition, for linear predictors, is in Granger, 1980. From Sargent: A stochastic process z_{t} is said NOT to Grangercause a random process x_{t} if E(x_{t+1}  x_{t},x_{t1},...,z_{t},z_{t1},...) = E(x_{t+1}  x_{t},x_{t1},...) *** NOTE in J Pehkonen, Applied Economics, 1991, 23, 15591568, p. 1560. *** Expert treatment of this subject and more formal, less ambiguous definitions are in Chamberlain, Econometrica, May 82

Grenander conditions
Conditions on the regressors under which the OLS estimator will be consistent.
The Grenander conditions are weaker than the assumption on the regressor X that lim_{n>infinity}(X'X)/n is a fixed positive definite matrix, which is a common starting assumption.
See Greene, 2nd ed, 1993, p 295.

Gresham's Law
Some version of "Bad money will drive out good." I think the context is that if there are two suppliers of the same money (e.g. if one of them is a counterfeiter) or of two monies with a fixed exchange rate between them (per Hayek, Denationalization of Money, 1976 p. 39), there will be a tendency for overproduction and that the actual money stock will be made up of the bad, or less valuable, one. (Another situation is if one supplier makes coins that are 90% gold and the other has the option of making coins with less gold, Bertrand competition for coins would drive the gold fraction down over time.)

GSOEP
German SocioEconomic Panel. A German government database going back to at least 1984.
