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620-262Decision Making

620-262Decision Making

Lecturer: Dr.Vicky MakRoom: 147 Richard Berry

Buildingemail:

vmak@ms.unimelb.edu.auphone: 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