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620-262Decision Making
620-262Decision Making
Lecturer: Dr.Vicky MakRoom: 147 Richard Berry
Buildingemail:
[email protected]: 83445558
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Students should note that, in lectures, many examples and additional comments will supplement these slides.
One or two topics to be covered in lectures (and examined) are not included in the slides at all.
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Prerequisite
Prerequisite
620-261
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Classes
Classes
Lectures: (Russell Love Theatre) Monday 4.15 – 5.15 Wednesday 4.15 – 5.15 Friday 4.15 – 5.15
Tutorials: One ofMonday 2.15 - 3.15 (Room D)Monday 3.15 - 4.15 (Room D)Wednesday 2.15 - 3.15 (Room D)Wednesday 3.15 - 4.15 (Room D)
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Assessment
Assessment
Assignments: 10% 10 equally weighted assignments,approximately weekly.
See later lectures for details.Must see me for any extensionsExam: one 3 hour exam, 90%
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Objectives
Objectives
See also notes or notice board for more detail.
Brief version:
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Comprehend: features of decision making situations in Operations Research and associated mathematical approaches and techniques;
theoretical foundations and practical issues.Develop:
skills to solve certain decision making problems (will use, in part, techniques from 261)
Appreciate: extent, limitations and subjective nature of some techniques/solutions.
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Lecture Notes
Lecture Notes
On Sale in University Bookroom ,
All topics are covered in the printed notes.
Additional handouts will be given in class.
Also keep checking website for additional info.
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Winston, WL: Operations research Applications and algorithms. Useful for some of subject only.10 copies, reserve desk, Maths & Stats Library
See notes, lectures and problem sheets for further references
References
References
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Web SiteWeb Site
Via Maths & Stats home pageclickStudent infoLecture material620-262
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Student Representative
Student Representative
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Topics
Topics
Game Theoryzero-sum 2-person gamesnon-zero-sum gamesn-person gamesPrisoner’s Dilemma
Multicriteria Decision making with use ofLinear ProgrammingDynamic Programming
Markovian Decision Processes with use ofLinear Programming
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What is Decision Making ?
What is Decision Making ?
... Men with the ability and courage to make major decisions and live with them are rare. In fact, to a large measure, the status of a man in the world of business and government is determined by the scope and importance of the decisions he is instructed to make.
Decision making is the central coordinating concept of any organization, whether it is a family farm business, a giant industrial complex, or a government agency ...
Halter and Dean, 1971
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. . . designed for normally intelligent people who want to think hard and systematically about some important real problems.
The theory of decision analysis is designed to help the individual make a choice among a set of prespecified alternatives....
Keeny and Raiffa
1976
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Why should you be interested in
“Good Decision Making”????
Why should you be interested in
“Good Decision Making”????
Be in a better position to comment on and criticize the decision making of others.
Not everyone is a good decision-maker.Most people are not “good” decision
makers. We need to make decisions all the time.
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Relation to 620-261
Relation to 620-261
Recall that in 620-261 we examined optimization problems of the form:
z := { opt ƒ(x) : x in X}where opt is either min or max ƒ is a real valued functionIn 620-262 we take a much broader view of decision making situations.
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Relation to Management StructureRelation to Management StructureRelation to Management StructureRelation to Management Structure
{ Philosophies
{ Techniques620-261
620-262
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The Nobel ConnectionThe Nobel Connection
Peace Literature
Chemistry and Physics Physiology and Medicine
Economic
Sciences
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1972 1972 The prize was awarded jointly to
Sir John R. Hicks and
Kenneth J. Arrow
for their pioneering contributions to
economic equilibrium theory and welfare theory.
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The prize was awarded jointly to
Leonid Vitaliykvich Kantorovich and Tjalling C. Koopmans
for their contributions to
optimum allocation of resources
1975 1975 1975 1975
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The prize was awarded jointly to
Harry N. Markowitz, Merton M. Miller and William F. Sharpe
for their pioneering work in the theory of financial economics.
1990199019901990
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1994 1994
The prize was awarded jointly to
John Harsanyi, John F. Nash and Reinhard Selten
for their pioneering analysis of equilibria in the theory of
non-cooperative games.
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Game TheoryGame Theory
Foundation:
Theory of Games and Economic Behaviour
J.von Neumann and O. Morgenstern
Princeton University Press, Princeton NJ, 1944
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Game TheoryGame Theory
Dynamic, expanding fieldInterest from
economistsmathematiciansbiologyfinance social sciences
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The Age Business section (? 1997) The dismal science out of favour but
still ruling the world (refers to economics!)
“… Game theory is finally delivering on its promises. It was used to design the highly successful auction of the radio spectrum this year and is working its way into all sorts of corporate decision-making in which one company must anticipate the competitive response of others.”
Peter Passell, New York Times
Quotes
Quotes
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The Age, Living Science section, 2 July 1998:The mating gene.
“… It is possible to make sense of sexual behaviour using a branch of mathematics called game theory, which provides a quantitative cost-benefit analysis for various sexual strategies…” Paul Davies
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Familiar ideas of games
Familiar ideas of games
playerssequence of moves
chance players skill mixture of chance / skill roulette, chess, bridge
payoff$money, prestige, satisfaction, etc.
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Other features of Game Land
Other features of Game Land
Number of players 2, 3, ....., n
Level of cooperationCooperativenon-cooperativecompetitive
Dynamicsstaticsequential
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There are at least two players. A player may be an individual, a company, a nation, a biological species, nature, etc.
Each player has a number of possible strategies, that is courses of action they can follow.
The strategies the players follow determine the outcome of the game.
Associated with each outcome is a payoff to each player i. e. the value of the outcome to each player. (From P.D. Straffin Game Theory & Strategy)
So, what is a game?So, what is a game?
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Example
Example
Matching pennies
Player A chooses heads (H) or tails (T). Player B, not knowing A’s choice, chooses H or T. If they choose the same, A wins 1 cent from B, otherwise B wins 1 cent from A.
What we are interested in is:
What strategy is best from the point of view of maximizing a player’s share of the payoff?
See lecture for mathematical set up of this problem.
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2-Person Games
2-Person Games
2 Players, groups, organisations, teams Game can be competitive or cooperative
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Equilibrium or Stable A (row, column) pair is said to be in equilibrium or stable if neither player has any incentive to change his/her decision given that the other player does not change her/his decision.
Basic ConceptBasic ConceptBasic ConceptBasic Concept