Production Possibilities
Frontier
In economics, a production possibilities curve (PPC) or “transformation
curve” is a graph that shows the different quantities of two
goods that an economy (or agent) could efficiently produce with
limited productive resources. Points along the curve describe the
trade-off between the two goods. The curve illustrates that increasing
production of one good reduces maximum production of the other good
as resources are transferred away from the other good.
Supply and demand
The price P of a product is determined by a balance between production
at each price (supply S) and the desires of those with purchasing
power at each price (demand D). The graph depicts an increase in
demand from D1 to D2, along with a consequent increase in price
and quantity Q sold of the product.
In economics, supply
and demand describe market relations between prospective sellers
and buyers of a good. The supply and demand model determines price
and quantity sold in the market. The model is fundamental in microeconomic
analysis of buyers and sellers and of their interactions in a market.
It is also used as a point of departure for other economic models
and theories. The model predicts that in a competitive market, price
will function to equalize the quantity demanded by consumers and
the quantity supplied by producers, resulting in an economic equilibrium
of price and quantity.
Fundamental theory
The intersection of supply and demand determines equilibrium price
and quantity.
Strictly considered,
the model applies to a type of market called perfect competition
in which no single buyer or seller has much effect on prices and
prices are known. The quantity of a product supplied by the producer
and the quantity demanded by the consumer are dependent on the market
price of the product. The law of supply states that quantity supplied
is related to price. It is often depicted as directly proportional
to price: the higher the price of the product, the more the producer
will supply, ceteris paribus. The law of demand is normally depicted
as an inverse relation of quantity demanded and price: the higher
the price of the product, the less the consumer will demand, cet.
par. "Cet. par." is added to isolate the effect of price.
Everything else that could affect supply or demand except price
is held constant. The respective relations are called the 'supply
curve' and 'demand curve', or 'supply' and 'demand' for short.
The laws of supply and
demand state that the equilibrium market price and quantity of a
commodity is at the intersection of consumer demand and producer
supply. Here quantity supplied equals quantity demanded (as in the
enlargeable Figure), that is, equilibrium. Equilibrium implies that
price and quantity will remain there if it begins there. If the
price for a good is below equilibrium, consumers demand more of
the good than producers are prepared to supply. This defines a shortage
of the good. A shortage results in the price being bid up. Producers
will increase the price until it reaches equilibrium. Conversely,
if the price for a good is above equilibrium, there is a surplus
of the good. Producers are motivated to eliminate the surplus by
lowering the price. The price falls until it reaches equilibrium.
Supply schedule
The supply schedule is the relationship between the quantity of
goods supplied by the producers of a good and the current market
price. It is graphically represented by the supply curve. It is
commonly represented as directly proportional to price.[1] The positive
slope in short-run analysis can reflect the law of diminishing marginal
returns, which states that beyond some level of output, additional
units of output require larger doses of the variable input. In the
long run (such that plant size or number of firms is variable),
a positively-sloped supply curve can reflect diseconomies of scale
or fixity of specialized resources (such as farm land or skilled
labor).
For a given firm in
a perfectly competitive industry, if it is more profitable to produce
at all, profit is maximized by producing to where price is equal
to the producer's marginal cost curve. Thus, the supply curve for
the entire market can be expressed as the sum of the marginal cost
curves of the individual producers.[2]
Demand schedule
The demand schedule, depicted graphically as the demand curve, represents
the amount of a good that buyers are willing and able to purchase
at various prices, assuming all other non-price factors remain the
same. The demand curve is almost always represented as downwards-sloping,
meaning that as price decreases, consumers will buy more of the
good.
Just as the supply curves
reflect marginal cost curves, demand curves be described as marginal
utility curves.
The main determinants
of individual demand are the price of the good, level of income,
personal tastes, the price of substitute goods, and the price of
complementary goods.
The shape of the aggregate
demand curve can be convex or concave, possibly depending on income
distribution.
Changes in market equilibrium
Practical uses of supply and demand analysis often center on the
different variables that change equilibrium price and quantity,
represented as shifts in the respective curves. Comparative statics
of such a shift traces the effects from the initial eqilibrium to
the new equilibrium.
Demand curve shifts
An out- or right- shift in demand changes the equilibrium price
and quantity
People increasing the
quantity demanded at a given price is be referred to as an increase
in demand. Increased demand can be represented on the graph as the
curve being shifted right, because at each price point, a greater
quantity is demanded, as from the initial curve D1 to the new curve
D2. An example of this would be more people suddenly wanting more
coffee. In the diagram, this raises the equilibrium price from P1
to the higher P2. This raises the equilibrium quantity from Q1 to
the higher Q2. In standard usage, a movement along a given demand
curve can be described as a "change in the quantity demanded"
to distinguish it from a "change in demand," that is,
a shift of the curve. In the example above, there has been an increase
in demand which has caused an in increase in ( (equilbrium) quantity.
The increase in demand could also come from changing tastes, incomes,
product information, fashions, and so forth.
Conversely, if the demand
decreases, the opposite happens: a lefward shift of the curve. If
the demand starts at D2 and then decreases to D1, the price will
decrease and the quantity will decrease&mdash. Notice that this
is purely an effect of demand changing. The quantity supplied at
each price is the same as before the demand shift (at both Q1 and
Q2). The reason that the equilibrium quantity and price are different
is the demand is different. At each point a greater amount is demanded
(when there is a shift from D1 to D2).
Supply curve shifts
An out- or right- shift in supply changes the equilibrium price
and quantity
When the suppliers'
costs change for a given output, the supply curve shifts in the
same direction. For example, assume that someone invents a better
way of growing wheat so that the cost of wheat that can be grown
for a given quantity will decrease. Otherwise stated, producers
will be willing to supply more wheat at every price and this shifts
the supply curve S1 to the right, to S2—an increase in supply.
This increase in supply causes the equilibrium price to decrease
from P1 to P2. The equilibrium quantity increases from Q1 to Q2
as the quantity demanded increases at the new lower prices. Notice
that in the case of a supply curve shift, the price and the quantity
move in opposite directions.
Conversely, if the quantity
supplied decreases at a given price, the opposite happens. If the
supply curve starts at S2 and then shifts leftward to S1, the equilibrium
price will increase and the quantity will decrease. This is purely
an effect of supply changing. The quantity demanded at each price
is the same as before the supply shift (at both Q1 and Q2). The
reason that the equilibrium quantity and price are different is
the supply changed.
There are only 4 possible
movements to a demand/supply curve diagram. The demand curve can
move to the left and right, and the supply curve can also move only
to the left or right. If they do not move at all then they will
stay in the middle where they already are.
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Elasticity
An important concept in understanding supply and demand theory is
elasticity. In this context, it refers to how supply and demand
change in response to various stimuli. One way of defining elasticity
is the percentage change in one variable divided by the percentage
change in another variable (known as arc elasticity because it calculates
the elasticity over a range of values, in contrast with point elasticity
that uses differential calculus to determine the elasticity at a
specific point). Thus it is a measure of relative changes.
Often, it is useful
to know how the quantity demanded or supplied will change when the
price changes. This is known as the price elasticity of demand and
the price elasticity of supply. If a monopolist decides to increase
the price of their product, how will this affect their sales revenue?
Will the increased unit price offset the likely decrease in sales
volume? If a government imposes a tax on a good, thereby increasing
the effective price, how will this affect the quantity demanded?
If you do not wish to
calculate elasticity, a simpler technique is to look at the slope
of the curve. Unfortunately, this has units of measurement of quantity
over monetary unit (for example, liters per euro, or battleships
per million yen), which is not a convenient measure to use for most
purposes. So, for example, if you wanted to compare the effect of
a price change of gasoline in Europe versus the United States, there
is a complicated conversion between gallons per dollar and liters
per euro. This is one of the reasons why economists often use relative
changes in percentages, or elasticity. Another reason is that elasticity
is more than just the slope of the function: It is the slope of
a function in a coordinate space, that is, a line with a constant
slope will have different elasticity at various points.
Elasticity in relation
to variables other than price can also be considered. One of the
most common to consider is income. How would the demand for a good
change if income increased or decreased? This is known as the income
elasticity of demand. For example, how much would the demand for
a luxury car increase if average income increased by 10%? If it
is positive, this increase in demand would be represented on a graph
by a positive shift in the demand curve, because at all price levels,
a greater quantity of luxury cars would be demanded.
Another elasticity that
is sometimes considered is the cross elasticity of demand, which
measures the responsiveness of the quantity demanded of a good to
a change in the price of another good. This is often considered
when looking at the relative changes in demand when studying complement
and substitute goods. Complement goods are goods that are typically
utilized together, where if one is consumed, usually the other is
also. Substitute goods are those where one can be substituted for
the other, and if the price of one good rises, one may purchase
less of it and instead purchase its substitute.
Cross elasticity of
demand is measured as the percentage change in demand for the first
good that occurs in response to a percentage change in price of
the second good. For an example with a complement good, if, in response
to a 10% increase in the price of fuel, the quantity of new cars
demanded decreased by 20%, the cross elasticity of demand would
be -20%/10% or, -2.
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Utility
In economics, utility is a measure of the relative happiness or
satisfaction (gratification) gained. Given this measure, one may
speak meaningfully of increasing or decreasing utility, and thereby
explain economic behavior in terms of attempts to increase one's
utility. The theoretical unit of measurement for utility is the
util.
The doctrine of utilitarianism
saw the maximization of utility as a moral criterion for the organization
of society. According to utilitarians, such as Jeremy Bentham (1748-1832)
and John Stuart Mill (1806-1876), society should aim to maximize
the total utility of individuals, aiming for "the greatest
happiness for the greatest number".
In neoclassical economics,
rationality is precisely defined in terms of imputed utility-maximizing
behavior under economic constraints. As a hypothetical behavioral
measure, utility does not require attribution of mental states suggested
by "happiness", "satisfaction", etc.
Utility is applied by
economists in such constructs as the indifference curve, which plots
the combination of commodities that an individual or a society requires
to maintain a given level of satisfaction. Individual utility and
social utility can be construed as the dependent variable of a utility
function (such as an indifference curve map) and a social welfare
function respectively. When coupled with production or commodity
constraints, these functions can represent Pareto efficiency, such
as illustrated by Edgeworth boxes and contract curves. Such efficiency
is a central concept of welfare economics.
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Output
Output in economics is the total value of all of the goods and services
produced in an entity's economy. It is a concept used in macroeconomics,
or the study of the economic transactions of broad groups such as
countries.
Net output, sometimes
called netput is a quantity, in the context of production, that
is positive if the quantity is output by the production process
and negative if it is an input to the production process.
Marginal cost
In economics and finance, marginal cost is the change in total cost
that arises when the quantity produced changes by one unit. Mathematically,
the marginal cost (MC) function is expressed as the derivative of
the total cost (TC) function with respect to quantity (Q). Note
that the marginal cost may change with volume, and so at each level
of production, the marginal cost is the cost of the next unit produced.
In general terms, marginal
cost at each level of production includes any additional costs required
to produce the next unit. If producing additional vehicles requires,
for example, building a new factory, the marginal cost of those
extra vehicles includes the cost of the new factory. In practice,
the analysis is segregated into short and long-run cases, and over
the longest run, all costs are marginal. At each level of production
and time period being considered, marginal costs include all costs
which vary with the level of production, and other costs are considered
fixed costs.
It is a general principle
of economics that a (rational) producer should always produce (and
sell) the last unit if the marginal cost is less than the market
price. As the market price will be dictated by supply and demand,
it leads to the conclusion that marginal cost equals marginal revenue.
These general principles are subject to a number of other factors
and exceptions, but marginal cost and marginal cost pricing play
a central role in economic definitions of efficiency.
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Externalities
Externalities are costs (or benefits) that are not borne by the
parties to the economic transaction. A producer may, for example,
pollute the environment, and others may bear those costs. A consumer
may consume a good which produces benefits for society, such as
education; because the individual does not receive all of the benefits,
he may consume less than efficiency would suggest. Alternatively,
an individual may be a smoker or alcoholic and impose costs on others.
In these cases, production or consumption of the good in question
may differ from the optimum level.
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Profit maximization
In economics, profit maximization is the process by which a firm
determines the price and output level that returns the greatest
profit. There are several approaches to this problem. The total
revenue -- total cost method relies on the fact that profit equals
revenue minus cost, and the marginal revenue -- marginal cost method
is based on the fact that total profit in a perfectly competitive
market reaches its maximum point where marginal revenue equals marginal
cost.
Diminishing returns
In economics, diminishing returns is also called diminishing marginal
returns or the law of diminishing returns. According to this relationship,
in a production system with fixed and variable inputs (say factory
size and labor), beyond some point, each additional unit of variable
input yields less and less additional output. Conversely, producing
one more unit of output costs more and more in variable inputs.
This concept is also known as the law of increasing relative cost,
or law of increasing opportunity cost. Although ostensibly a purely
economic concept, diminishing marginal returns also implies a technological
relationship. Diminishing marginal returns states that a firm's
short run marginal cost curve will eventually increase. It is possibly
among the best-known economic "laws."
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Monopoly
A monopoly (from the Greek language monos, one + polein, to sell)
is defined as a persistent market situation where there is only
one provider of a product or service, in other words a firm that
has no competitors in its industry. Monopolies are characterized
by a lack of economic competition for the good or service that they
provide and a lack of viable substitute goods. [1]
Monopoly should be distinguished
from monopsony, in which there is only one buyer of the product
or service; monopolies often have monopsony control of a sector
of a market. Likewise, monopoly should also be distinguished from
the phenomenon of a cartel. In a monopoly a single firm is the sole
provider of a product or service; in a cartel a centralized institution
is set up to partially coordinate the actions of several independent
providers (which is a form of oligopoly).
A government-granted
monopoly, or legal monopoly is sanctioned by the state, often to
provide a greater reward and incentive to invest in a risky venture.
The government may also reserve the venture for itself, which is
called a government monopoly.
If a monopoly is not
protected from competition by law, then it is subject to competitive
forces. However, with enough market share, a company or group can
partially plan and control the market through strategic product
updates or lower prices - potential competition can be thwarted,
while demand for the dominant company's output can be preferentially
developed. Hence, within free economies, planned sub-economies can
arise.
Primary characteristics
of a monopoly
Single Seller: For a pure monopoly to take place, only one company
can be selling the good or service. A company can have a monopoly
on certain goods and services but not on others.
Significant Barrier
of Entry: If a company has a monopoly on a good or service, it becomes
prohibitively difficult for other firms to enter the industry and
provide the same good or service.
No close substitutes:
Monopoly is not merely the state of having control over a product;
it also means that there are no close substitutes available that
fill the same function as the monopolized good.
Price maker: Because
a single firm controls the total supply in a pure monopoly, it is
able to exert a significant degree of control over the price by
changing the quantity supplied.
The "natural monopoly"
problem
A natural monopoly is defined as a situation in which production
is characterized by falling long-run marginal cost throughout the
relevant output range. In such situations, a policy of laissez-faire
must result in a single seller. The conventional Paretian solution
to market failure of this kind is public regulation (in USA) or
public enterprise (in United Kingdom). Liberals reject both alternatives
as being incompatible with important freedoms.[5].
An oligopoly is a market
form in which a market or industry is dominated by a small number
of sellers (oligopolists). The word is derived from the Greek for
few sellers. Because there are few participants in this type of
market, each oligopolist is aware of the actions of the others.
Oligopolistic markets are characterised by interactivity. The decisions
of one firm influence, and are influenced by the decisions of other
firms. Strategic planning by oligopolists always involves taking
into account the likely responses of the other market participants.
This causes oligopolistic markets and industries to be at the highest
risk for collusion.
Oligopoly
Oligopoly is a common
market form. As a quantitative description of oligopoly, the four-firm
concentration ratio is often utilized. This measure expresses the
market share of the four largest firms in an industry as a percentage.
Using this measure, an oligopoly is defined as a market in which
the four-firm concentration ratio is above 40%. For example, the
four-firm concentration ratio of the supermarket industry in the
United Kingdom is over 70%; the British brewing industry has a staggering
85% ratio. In the U.S.A, oligopolistic industries include accounting
& audit services, tobacco, beer, aircraft, military equipment,
motor vehicle, film and music recording industries.
In an oligopoly, firms
operate under imperfect competition and a kinked demand curve which
reflects inelasticity below market price and elasticity above market
price, the product or service firms offer, are differentiated and
barriers to entry are strong. Following from the fierce price competitiveness
created by this sticky-upward demand curve, firms utilize non-price
competition in order to accrue greater revenue and market share.
Oligopolistic competition
can give rise to a wide range of different outcomes. In some situations,
the firms may collude to raise prices and restrict production in
the same way as a monopoly. Where there is a formal agreement for
such collusion, this is known as a cartel.
Firms often collude
in an attempt to stabilise unstable markets, so as to reduce the
risks inherent in these markets for investment and product development.
There are legal restrictions on such collusion in most countries.
There does not have to be a formal agreement for collusion to take
place (although for the act to be illegal there must be a real communication
between companies) - for example, in some industries, there may
be an acknowledged market leader which informally sets prices to
which other producers respond, known as price leadership.
In other situations,
competition between sellers in an oligopoly can be fierce, with
relatively low prices and high production. This could lead to an
efficient outcome approaching perfect competition. The competition
in an oligopoly can be greater than when there are more firms in
an industry if for example the firms were only regionally based
and didn't compete directly with each other.
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Game theory
Game theory is often described as a branch of applied mathematics
and economics that studies situations where multiple players make
decisions in an attempt to maximize their returns. The essential
feature is that it provides a formal modelling approach to social
situations in which decision makers interact with other agents.
Game theory extends the simpler optimisation approach developed
in neoclassical economics.
The field of game theory
came into being with the 1944 classic Theory of Games and Economic
Behavior by John von Neumann and Oskar Morgenstern. A major center
for the development of game theory was RAND Corporation where it
helped to define nuclear strategies.
Game theory has played,
and continues to play a large role in the social sciences, and is
now also used in many diverse academic fields. Beginning in the
1970s, game theory has been applied to animal behaviour, including
evolutionary theory. Many games, especially the prisoner's dilemma,
are used to illustrate ideas in political science and ethics. Game
theory has recently drawn attention from computer scientists because
of its use in artificial intelligence and cybernetics.
In addition to its academic
interest, game theory has received attention in popular culture.
A Nobel Prize–winning game theorist, John Nash, was the subject
of the 1998 biography by Sylvia Nasar and the 2001 film A Beautiful
Mind. Game theory was also a theme in the 1983 film WarGames. Several
game shows have adopted game theoretic situations, including Friend
or Foe? and to some extent Survivor. The character Jack Bristow
on the television show Alias is one of the few fictional game theorists
in popular culture.[1]
Although some game theoretic
analyses appear similar to decision theory, game theory studies
decisions made in an environment in which players interact. In other
words, game theory studies choice of optimal behavior when costs
and benefits of each option depend upon the choices of other individuals.
Applying game theory to procedures and organisation in real life
is often called gaming the system. This has a negative connotation
and usually implies disingenuous behaviour.
Infinitely long games
Games, as studied by economists and real-world game players, are
generally finished in a finite number of moves. Pure mathematicians
are not so constrained, and set theorists in particular study games
that last for infinitely many moves, with the winner (or other payoff)
not known until after all those moves are completed.
The focus of attention
is usually not so much on what is the best way to play such a game,
but simply on whether one or the other player has a winning strategy.
(It can be proven, using the axiom of choice, that there are games
— even with perfect information, and where the only outcomes
are "win" or "lose" — for which neither
player has a winning strategy.) The existence of such strategies,
for cleverly designed games, has important consequences in descriptive
set theory.
Application and challenges
of game theory
Games in one form or another are widely used in many different disciplines.
Political science
The application of game theory to political science is focused in
the overlapping areas of fair division, political economy, public
choice, positive political theory, and social choice theory. In
each of these areas, researchers have developed game theoretic models
in which the players are often voters, states, interest groups,
and politicians.
For early examples of
game theory applied to political science, see the work of Anthony
Downs. In his book An Economic Theory of Democracy (1957), he applies
a Hotelling firm location model to the political process. In the
Downsian model, political candidates commit to ideologies on a one-dimensional
policy space. The theorist shows how the political candidates will
converge to the ideology preferred by the median voter. For more
recent examples, see the books by George Tsebelis, Gene M. Grossman
and Elhanan Helpman, or David Austen-Smith and Jeffrey S. Banks.
Game theory provides
a theoretical description for a variety of observable consequences
of changes in governmental policies. For example, in a static world
where producers were not themselves decision makers attempting to
optimize their own expenditure of resources while assuming risks,
response to an increase in tax rates would imply an increase in
revenues and vice versa. Game Theory inclusively weights the decision
making of all participants and thus explains the contrary results
illustrated by the Laffer Curve.
Economics and business
Economists have long used game theory to analyze a wide array of
economic phenomena, including auctions, bargaining, duopolies, fair
division, oligopolies, social network formation, and voting systems.
This research usually focuses on particular sets of strategies known
as equilibria in games. These "solution concepts" are
usually based on what is required by norms of rationality. The most
famous of these is the Nash equilibrium. A set of strategies is
a Nash equilibrium if each represents a best response to the other
strategies. So, if all the players are playing the strategies in
a Nash equilibrium, they have no unilateral incentive to deviate,
since their strategy is the best they can do given what others are
doing.
The payoffs of the game
are generally taken to represent the utility of individual players.
Often in modeling situations the payoffs represent money, which
presumably corresponds to an individual's utility. This assumption,
however, can be faulty.
A prototypical paper
on game theory in economics begins by presenting a game that is
an abstraction of some particular economic situation. One or more
solution concepts are chosen, and the author demonstrates which
strategy sets in the presented game are equilibria of the appropriate
type. Naturally one might wonder to what use should this information
be put. Economists and business professors suggest two primary uses.
Game theory has been
put to several uses in philosophy. Responding to two papers by W.V.O.
Quine (1960, 1967), David Lewis (1969) used game theory to develop
a philosophical account of convention. In so doing, he provided
the first analysis of common knowledge and employed it in analyzing
play in coordination games. In addition, he first suggested that
one can understand meaning in terms of signaling games. This later
suggestion has been pursued by several philosophers since Lewis
(Skyrms 1996, Grim et al. 2004).
In ethics, some authors
have attempted to pursue the project, begun by Thomas Hobbes, of
deriving morality from self-interest. Since games like the Prisoner's
Dilemma present an apparent conflict between morality and self-interest,
explaining why cooperation is required by self-interest is an important
component of this project. This general strategy is a component
of the general social contract view in political philosophy (for
examples, see Gauthier 1987 and Kavka 1986).[4]
Other authors have attempted
to use evolutionary game theory in order to explain the emergence
of human attitudes about morality and corresponding animal behaviors.
These authors look at several games including the Prisoner's Dilemma,
Stag hunt, and the Nash bargaining game as providing an explanation
for the emergence of attitudes about morality (see, e.g., Skyrms
1996, 2004; Sober and Wilson 1999).
History of game theory
The first known discussion of game theory occurred in a letter written
by James Waldegrave in 1713. In this letter, Waldegrave provides
a minimax mixed strategy solution to a two-person version of the
card game le Her. It was not until the publication of Antoine Augustin
Cournot's Researches into the Mathematical Principles of the Theory
of Wealth in 1838 that a general game theoretic analysis was pursued.
In this work Cournot considers a duopoly and presents a solution
that is a restricted version of the Nash equilibrium.
Although Cournot's analysis
is more general than Waldegrave's, game theory did not really exist
as a unique field until John von Neumann published a series of papers
in 1928. While the French mathematician Borel did some earlier work
on games, Von Neumann can rightfully be credited as the inventor
of game theory. Von Neumann was a brilliant mathematician whose
work was far-reaching from set theory to his calculations that were
key to development of both the Atom and Hydrogen bombs and finally
to his work developing computers. Von Neumann's work in game theory
culminated in the 1944 book The Theory of Games and Economic Behavior
by von Neumann and Oskar Morgenstern. This profound work contains
the method for finding optimal solutions for two-person zero-sum
games. During this time period, work on game theory was primarily
focused on cooperative game theory, which analyzes optimal strategies
for groups of individuals, presuming that they can enforce agreements
between them about proper strategies.
In 1950, the first discussion
of the prisoner's dilemma appeared, and an experiment was undertaken
on this game at the RAND corporation. Around this same time, John
Nash developed a definition of an "optimum" strategy for
multiplayer games where no such optimum was previously defined,
known as Nash equilibrium. This equilibrium is sufficiently general,
allowing for the analysis of non-cooperative games in addition to
cooperative ones.
Game theory experienced
a flurry of activity in the 1950s, during which time the concepts
of the core, the extensive form game, fictitious play, repeated
games, and the Shapley value were developed. In addition, the first
applications of Game theory to philosophy and political science
occurred during this time.
In 1965, Reinhard Selten
introduced his solution concept of subgame perfect equilibria, which
further refined the Nash equilibrium (later he would introduce trembling
hand perfection as well). In 1967, John Harsanyi developed the concepts
of complete information and Bayesian games. Nash, Selten and Harsanyi
became Economics Nobel Laureates in 1994 for their contributions
to economic game theory.
In the 1970s, game theory
was extensively applied in biology, largely as a result of the work
of John Maynard Smith and his evolutionary stable strategy. In addition,
the concepts of correlated equilibrium, trembling hand perfection,
and common knowledge[6] were introduced and analysed.
In 2005, game theorists
Thomas Schelling and Robert Aumann followed Nash, Selten and Harsanyi
as Nobel Laureates. Schelling worked on dynamic models, early examples
of evolutionary game theory. Aumann contributed more to the equilibrium
school, developing an equilibrium coarsening correlated equilibrium
and developing extensive analysis of the assumption of common knowledge.
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