Добавил:
ivanov666
Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз:
Предмет:
Файл:Economics in Construction. Учебное пособие
.pdf
game theory studies choice of optimal behaviour when costs and benefits of
Player 2 chooses left
Player 2 chooses right
Player 1 chooses top
4,3
-1, -1
Player 1 chooses
bottom
0,0
3,4
each option are not fixed, but depend upon the choices of other individuals.
The games studied by 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 payoffs for each combination of strategies.
There are two ways of representing games that are common in the literature.
A normal form game
The normal (or strategic form) game is a matrix which shows the players,
strategies, and payoffs (see the example to the right). Here there are two players;
one chooses the row and the other chooses the column. Each player has two
strategies, which arc specified by the number of rows and the number of
columns. The payoffs are provided in the interior. The first number is the payoff
received by the row player (Player l in our example); the second is the payoff for
the column player (Player 2 in our example). Suppose that Player 1 plays top
and that Player 2 plays left. Then Player 1 gets 4, and Player 2 gets 3.
When a game is presented in normal form, it is presumed that each player
acts simultaneously or, at least, without knowing the actions of the other. If
players have some information about the choices of other players, the game is
usually presented in extensive form.
Extensive form games attempt to capture games with some important
order. Games here are presented as trees (as pictured to the left). Here each
vertex (or node) represents a point of choice for a player. The player is specified
41
by a number listed by the vertex. The lines out of the vertex represent a possible
action for that player. The payoffs are specified at the bottom of the tree.
In the game pictured here, there are two players. Player 1 moves first and
chooses either F or U. Player 2 sees Player l's move and then chooses A or R.
Suppose that Player 1 chooses U and then Player 2 chooses A, then Player 1 gets
8 and Player 2 gets 2.
Extensive form games can also capture simultaneous-move games as well.
Either a dotted line or circle is drawn around two different vertices to represent
them as being part of the same information set (i.e., the players do not know at
which point they are).
Extensive form game
There are several types of games: a symmetric game, zero sum and non-
zero sum, simultaneous and sequential, perfect information and imperfect
information, infinitely long games.
Economists have used game theory to analyze a wide array of economic
phenomena, including auctions, bargaining, duopolies and oligopolies, social
network formation, and voting systems. This research usually focuses on
particular sets of strategies known as equilibrium 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
42
incentive to deviate, since their strategy is the best they can do given what others
are doing.
Game theory has come to play an increasingly important role in logic and
in computer science. Several logical theories have a basis in game semantics. In
addition, computer scientists have used games to model interactive
computations. It also plays an important role in biology and philosophy.
Source: C.E. Shannon, W. Weaver, The Mathematical Theory of Communication (2013)
GRAMMATICAL NOTES
tted line is drawn around two different vertices to represent them as
, чтобы представить их
как.
concept of mutual assured destruction
prisoner's dilemma
social network formation
natural selection
to presume
incentive to deviate
wide array
economic phenomena
auctions
VOCABULARY
bargaining
duopolies
43
oligopolies
to capture , ,
to invest
to model interactive computations
simultaneous
sequential
infinitely
to circulate
1. Give Russian equivalents to the following word combinations:
pplied mathematics; attempt to capture; mutual assured destruction;
artificial intelligence; diverse academic fields; a set of moves; optimal
behaviour; natural selection; mutual self-interest; due to application; substantial
growth; players interact; extensive form; a dotted line; vertex (or node); a wide
array of; economic phenomena; social network; interactive computations; to
w attention; Nash equilibrium; a set
of strategies; incentive to deviate; well-defined mathematical objects; a received
payoff; matrix; to be the subject of
2. Find in the text and give English equivalents to the following
word combinations:
44
3. Translate words and word combinations in bold and the whole
sentences:
1. A dotted line or circle is drawn around different вершин, чтобы
представить them as being part of the same information set.
2. Game theory is used in many academic spheres, including
формирование социальных сетей.
3. It is based on what требуется by norms of rationality.
4. Costs and benefits of each option не фиксированы, но зависят от
the choices of other individuals.
5. Economists использовали теорию игр для анализа a wide array of
economic phenomena, including auctions, bargaining, duopolies and
oligopolies, social network formation, and voting systems.
6. Computer scientists use game theory in искусственном интеллекте.
7. Вознаграждение указано at the bottom of the tree.
8. Game theory saw substantial growth, в основном благодаря ее
application to military strategy.
9. A game consists of a set of players, a set of moves (or strategies)
доступных для тех игроков, and a specification payoffs for each combination
of strategies.
10. They wanted наше внимание to this subject, but were not
interested in it.
4. Translate into English:
1.
45
.
.
5. Complete the sentences:
1. Mutual self-interest hurts everyone in ...
2. Matrix in game theory shows ...
3. Game theory has been applied to ...
4. Optimal behaviour is needed in every game, if you want ...
5. Friend or Foe and Survivor are two examples of ...
6. You try to maximize your returns in ...
7. One focuses on particular sets of strategies, if he ...
8. You need to offset expenditure when ....
9
46
them:
1. economic stimulus
package
a. a speech of encouragement
2. pep talk
b. basically good
3. fundamentally
healthy
c. time when the economy of a country is not very
successful
4. recession
c. a group of measures to activate business
5. a breach of
corporate confidence
d. misconduct by officials
6. malfeasance
f. a break in the trust people have for large businesses
7. output
g. production
8. issue
h. safety
9. acutely
i. intensely
10. security
j. an important problem that people are talking about
6. Answer the questions to the text:
1. What does game theory study?
2. Where is game theory applied to?
3. What does any game consist of?
4. What is Nash equilibrium?
7. Discuss the following:
1. Why is game theory now used in many diverse academic fields?
8. Match the words or phrases with their definitions and translate
9. Translate the text in a written form:
President Bush told reporters his economic stimulus package would be
aimed at creating jobs and taking care of those who couldn't find work. Though
47
he gave no details, White House officials say it's likely to mean more tax cuts
for businesses and individuals.
In something of a New Year's pep talk to investors, the president told
reporters that while measures were needed to enhance the US economy, it
remained fundamentally healthy: "This economy is pretty darned strong, given
the fact that we've been through a recession, and a terrorist attack, a breach of
corporate confidence because of some malfeasance, and yet the economy still
grows". But there are mixed signals about the direction the US economy is heading. Although there was a large increase in output from America's
manufacturers in December, there was also a rise in unemployment.
The economy is a vital issue for the Bush administration, with the White
House acutely aware that the president's chances of re-election in 2004 are
likely to depend as much on the voters' sense of financial, as well as physical,
security
10. Put questions to the words in bold and answer them.
11. Make up your own sentences using the words in bold.
12. Discuss the following:
of financial and physical security?
48
U N I T 6
A BEAUTIFUL MIND
(JOHN FORBES NASH)
John Forbes Nash Jr. (born June 13,
1928) is an American mathematician who
works in game theory and differential
geometry. He shared the 1994 Bank of Sweden
Prize in Economic Sciences in Memory of
Alfred Nobel with two other game theorists,
Reinhard Selten and John Harsanyi. The winner
of a Westinghouse scholarship, he attended the
Carnegie Institute of Technology, where he received both his bachelor's degree
and his master's degree in 1948. From Pittsburgh he went to Princeton
University where he worked on his equilibrium theory. He received a Ph.D. in
1950 with a dissertation on non-cooperative games. The thesis, which was
written under the supervision of Albert W. Tucker, contained the definition and
properties of what would later be called the Nash equilibrium.
At the Massachusetts Institute of Technology, he met Alicia Lopez-
Harrison de Larde, a math student from El Salvador, whom he married in
February' 1957. Their son, John Charles Martin (b. 1959), remained nameless
for a year because Alicia, having just committed Nash to a mental hospital, felt
that he should have a say in what to name the baby. John became a
mathematician, but, like his father, he was diagnosed a paranoid schizophrenic.
In 1958, Nash began to show the first signs of his mental illness. He became
paranoid and was admitted into the McLean Hospital, April-May 1959, where
49
he was diagnosed with paranoid schizophrenia. After a problematic stay in Paris
and Geneva, Nash returned to Princeton in 1960. He remained in and out of
mental hospitals until 1970, undergoing various treatments including insulin
shock therapy.
Some of his treatments may have worsened his condition because his
doctors did not realize the centrality of work and community to curing mental
illness; the most successful "treatment" seems to have been the administrative
decisions of Princeton's mathematics department and computer centre to allow
Nash to use university facilities for his research during this period, although the
research he conducted was initially delusional.
In student and on-campus legend, Nash became "The Phantom of Fine
Hall" (Fine Hall is Princeton's mathematics centre), a shadowy figure who
would scribble arcane equations on blackboards in the middle of the night. The
legend appears in a work of fiction based on Princeton life, "The Mind-Body
Problem", by Rebecca Goldstein.
Encouraged by his wife Alicia, Nash persisted in working in a com-
munitarian setting where his eccentricities were unremarked and developed,
among other interests, an interest in the calculation of exact values of large
numbers, researches which drove him to Princeton's Information Centres, where
he developed computer programs (of high quality) for his work. Here he had
more contact with Princetonians, which allowed Nash to further cope with his
mental illness.
He is best known in popular culture as the subject of the Hollywood
movie, A Beautiful Mind, about his mathematical genius and his struggles with
mental illness. The film A Beautiful Mind, released in 2001 and directed by Ron
Howard, was inspired by Nash's life and received four Academy Awards,
including Best Picture. It is loosely based on the biography of the same title by
Sylvia Nasar (1999), and has been criticized for its inaccurate portrayal of
50
Соседние файлы в предмете [НЕСОРТИРОВАННОЕ]