7.3 Движение декабристов (стр. 5 )

Nash equilibrium has been used to analyze hostile situations like war and arms races (see Prisoner’s dilemma), and also how conflict may be mitigated by repeated interaction (see Tit-for-tat). It has also been used to study to what extent people with different preferences can cooperate (see Battle of the sexes), and whether they will take risks to achieve a cooperative outcome (see Stag hunt). It has been used to study the adoption of technical standards, and also the occurrence of bank runs and currency crises (see Coordination game). Other applications include traffic flow (see Wardrop’s principle), how to organize auctions (see Auction theory), and even penalty kicks in soccer (see Matching pennies).

Game theory has been used to study a wide variety of human or animal behaviors. It was initially developed in economics to understand a large collection of economic behaviors, including behaviors of firms, markets, and consumers. The use of game theory in the social sciences has expanded and has been applied to political, sociological, and psychological behaviors as well.

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. Also, game theory provides a theoretical basis to the field of multi-agent systems.

The field of algorithmic game theory combines computer science concepts of complexity and algorithm design with game theory and economic theory. The emergence of the internet has motivated the development of algorithms for finding equilibria in games, markets, computational auctions, peer-to-peer systems, and security and information markets.

1 Say if the statements below are TRUE or FALSE:

1 Any player depends on other players’ choices due to game theory.

2 The equilibrium concept differs from one field of science to another.

3 Game theory came into being when the book by J. F. Nash appeared.

4 Game theorists have been welcomed by the Nobel prize committee.

5 Nash equilibrium cannot be applied to the military.

6 Game theory added much to computer science development.

7 Both humans and animals can be described by game theory.

2 Answer the questions:

1 What is a game from a mathematical and logical point of view?

2 What do you know about the history of game theory development?

3 What is the idea of the Nash equilibrium concept?

4 Who may benefit from the Nash equilibrium concept?

5 In what field is the demand for game theory increasingly high today?

3 Complete the list of Latin origin nouns by giving their singular or plural form:

___________ data

equilibrium ___________

formulae ___________

___________ criteria

___________ axes

___________ quanta

4 Give antonyms of the following words:

hostile explicitly cooperative normal

informal extensive to expand to mitigate

5 Use synonyms to explain the following words:

outcome insight standard scholar

currency concept to occur unilaterally

6 Fill in the blanks in the sentences below with the proper prepositions:

1 An individual success ____ making choices depends ____ the choices ____ others.

2 Game theory has been widely recognized ____ an important tool in many fields.

3 No player can benefit ____ changing his or her strategy.

4 Eight game theorists have won Nobel prizes ____ economics.

5 The developments ___ economics were later applied ____ biology largely ____ John Maynard Smith.

Unit 6

1 Do you often wait in a queue? When and where do you queue? How do you feel when waiting in a queue?

2 What is the main idea of queuing theory? Where can it be applied?

3 Make sure that you can read and understand the following words and word combinations from the text. Memorize them.

iteration finite to abandon

switchboard infinite to grant

entity discrete to exceed

customer viable to balk

server excessive to jockey

congestion manually

simulation randomly

4 Read the text

QUEUING THEORY

Queuing theory deals with problems which involve queuing (or waiting). Typical examples might be: banks/supermarkets (waiting for service), computers (waiting for a response), failure situations (waiting for a failure to occur e. g. in a piece of machinery), public transport (waiting for a train or a bus). As we know queues are a common everyday experience. They form because resources are limited. It makes economic sense to have queues just to know for example how many supermarket tills you would need to avoid queuing or how many buses or trains would be needed to avoid queues.

The first to develop a viable queuing theory was the French mathematician S. D. Poisson (1781-1840). He created a distribution function to describe the probability of a prescribed outcome after repeated iterations of independent trials. Poisson used a statistical approach. His distributions could be applied to any situation where excessive demands are made on a limited resource. The most important application of queuing theory occurred during the late 1800s, when telephone companies were faced with the problem of how many operators to place on duty at a given time. At the time, all calls were switched manually by an operator who physically connected a wire to a switchboard. A Danish mathematician named A. K Erlang developed a different approach to traffic engineering based on Poisson’s work. He established formulas for calls that are abandoned (called Erlang-B) and for those that are held until service is granted (Erlang-C).

All queuing systems can be broken into individual subsystems consisting of entities queuing for some activity. To analyze these subsystems we need information related to:

arrival process:

- how many customers arrive singly or in groups;

- how the arrivals are distributed in time (what is the probability distribution of time between successive arrivals – the interarrival time distribution);

- whether there is a finite population of customers or an infinite number.

service mechanism:

- a description of the resources needed for service to begin;

- how long the service will take (the service time distribution);

- the number of severs available;

- whether the servers are in series (each server has a separate queue) or in parallel (on queue for all servers);

- whether preemtion is allowed (a server can stop processing a customer to deal with another “emergency” customer).

queue characteristics:

- how, from a set of customers waiting for service, do we choose the one to be served next (FIFO - first-in first-out also known as FCFS –first-come first-served, LIFO – last-in first out, randomly);

- do we have balking (customers deciding not to join the queue if it is too long),

reneging (customers leave the queue if they have waited too long for a service),

jockeying (customers switch between queues if they think they will get faster by doing so);

a queue of finite capacity or of infinite capacity.

Changing the queue discipline (the rule by which we select the next customer to be served) can often reduce congestion.

In terms of the analysis of queuing situations the typical questions are:

- How long does a customer expect to wait in the queue before they are served, and how long will they have to wait before the service is complete?

- What is the probability of a customer having to wait longer than a given time interval before they are served?

- What is the average length of the queue?

- What is the probability that the queue will exceed a certain length? –

- What is the expected utilization of the server and the expected time period during which he will be fully occupied (servers cost money so we need them to keep busy).

In order to get answers to the above questions there are two basic approaches: analytic methods or formula based queuing theory and simulation or computer based queuing theory. Analytic methods are only available for relatively simple queuing plex queuing systems are almost always analyzed using simulation.

1 Say if the statements below are TRUE or FALSE:

1 Queuing is still a problem today.

2 The French scientist made the theoretical basis for queuing theory.

3 A. K. Erlang’s approach helped many telephone stations to solve their problems.

4 To solve a queuing problem one must build up its simplified model.

5 The customers are often served randomly.

6 Congestion is the result of an effective management.

7 Computation of queuing problems means their simulation.

2 Answer the questions.

1 Why is queuing theory in such demand today?

2 What did S. D. Poisson create?

3 What big application did queuing theory occur in 1800s?

4 What aspects must be considered when analyzing a queuing subsystem?

5 What parameters can arrival process include?

6 What does service mechanism consist of?

7 What do abbreviations FIFO and LIFO stand for?

8 What is the difference between balking, reneging and jockeying?

9 What is a queue discipline?

10 What points are especially important for any service manager?

l) What are two basic approaches in queuing theory?

3 Match the words with their definitions:

a) the person who receives a service entity

b) done with hands viable

c) pretence, imitation customer

d) the state of being too full, overcrowded distribution

e) to go away from, not intending

to return to congestion

f) to do again and again

h) the device for making or breaking

connection infinite

i) endless, without limits

j) putting, giving or sending out parts of a to iterate

set of things

k) money-register to abandon

l) able to exist manually

m) something that really exists simulation

4 Give synonyms or explain the meaning of the noun from the text:

iteration, distribution, application, population, simulation,

utilization

5 Find in the text the phrases or sentences that make the context for the following adverbs: