620-262 Decision Making

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DECISION MAKING 620-262
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620-262Decision Making

• Lecturer Dr.Vicky Mak
• Room 147 Richard Berry Building
• email vmak_at_ms.unimelb.edu.au
• phone [phone]

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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

• 620-261

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Classes

• Lectures (Russell Love Theatre)
• Monday 4.15 5.15
• Wednesday 4.15 5.15
• Friday 4.15 5.15
• Tutorials One of
• Monday 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

• Assignments 10
• 10 equally weighted assignments,approximately
  weekly.
• See later lectures for details.
• Must see me for any extensions
• Exam one 3 hour exam, 90

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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

• 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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References

• 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

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Web Site

• Via
• Maths Stats home page
• click
• Student info
• Lecture material
• 620-262

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Student Representative
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Topics

• Game Theory
• zero-sum 2-person games
• non-zero-sum games
• n-person games
• Prisoners Dilemma
• Multicriteria Decision making with use of
• Linear Programming
• Dynamic Programming
• Markovian Decision Processes with use of
• Linear Programming

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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????

• 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

• 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 function
• In 620-262 we take a much broader view of
  decision making situations.

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Relation to Management Structure

Philosophies
620-262

Techniques
620-261
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The Nobel Connection
Economic

• Peace

Literature
Sciences
Physiology and Medicine
Chemistry and Physics
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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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1975
The prize was awarded jointly to Leonid
Vitaliykvich Kantorovich and Tjalling C.
Koopmans for their contributions to optimum
allocation of resources
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1990
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.
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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 THEORY
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Game 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 Theory

• Dynamic, expanding field
• Interest from
• economists
• mathematicians
• biology
• finance
• social sciences

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Quotes

• 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

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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

• players
• sequence 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

• Number of players
• 2, 3, ....., n
• Level of cooperation
• Cooperative
• non-cooperative
• competitive
• Dynamics
• static
• sequential

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So, what is a game?

• 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)

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Example

• Matching pennies
• Player A chooses heads (H) or tails (T).
  Player B, not knowing As 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 players share of the payoff?
• See lecture for mathematical set up of this
  problem.

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2-Person Games

• 2 Players, groups, organisations, teams
• Game can be competitive or cooperative

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Basic Concept

• 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.