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2 620-262 Decision Making H Lecturer: Dr.Vicky Mak H Room: 147 Richard Berry Building H email: vmak@ms.unimelb.edu.au H phone: 83445558

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3 ª Students should note that, in lectures, many examples and additional comments will supplement these slides. ª One or two topics to be covered in lectures (and examined) are not included in the slides at all.

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4 Prerequisite H 620-261

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5 Classes H Lectures: (Russell Love Theatre) D Monday 4.15 – 5.15 D Wednesday 4.15 – 5.15 D Friday 4.15 – 5.15 Tutorials: One of DMonday 2.15 - 3.15 (Room D) DMonday 3.15 - 4.15 (Room D) DWednesday 2.15 - 3.15 (Room D) DWednesday 3.15 - 4.15 (Room D)

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6 Assessment H Assignments: 10% D 10 equally weighted assignments,approximately weekly. D See later lectures for details. D Must see me for any extensions H Exam: one 3 hour exam, 90%

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7 Objectives H See also notes or notice board for more detail. H Brief version:

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8 H Comprehend: Dfeatures of decision making situations in Operations Research and associated mathematical approaches and techniques; Dtheoretical foundations and practical issues. H Develop: Dskills to solve certain decision making problems (will use, in part, techniques from 261) H Appreciate: Dextent, limitations and subjective nature of some techniques/solutions.

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9 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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10 _ 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

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11 Web Site Via Maths & Stats home page click Student info Lecture material 620-262

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12 Student Representative

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13 Topics H Game Theory g zero-sum 2-person games g non-zero-sum games g n-person games g Prisoner’s Dilemma H Multicriteria Decision making with use of g Linear Programming g Dynamic Programming H Markovian Decision Processes with use of g Linear Programming

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14 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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15... 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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16 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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17 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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18 Relation to Management Structure { Philosophies { Techniques 620-261 620-262

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19 The Nobel Connection PeaceLiterature Chemistry and Physics Physiology and Medicine Economic Sciences

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20 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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21 The prize was awarded jointly to Leonid Vitaliykvich Kantorovich and Tjalling C. Koopmans for their contributions to optimum allocation of resources 19751975

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22 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. 19901990

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23 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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25 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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26 Game Theory H Dynamic, expanding field H Interest from C economists C mathematicians C biology C finance C social sciences

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27 S The Age Business section (? 1997) S 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

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28 W The Age, Living Science section, W 2 July 1998: W 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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29 Familiar ideas of games H players H sequence of moves ¤ chance « players skill ¨ mixture of chance / skill u roulette, chess, bridge H payoff $ money, prestige, satisfaction, etc.

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30 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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31 ¨ 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?

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32 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. F 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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33 2-Person Games 2 Players, groups, organisations, teams Game can be competitive or cooperative

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34 H 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 Concept

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