Game Theory
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MODULE
4
Game Theory
LEARNING OBJECTIVES
After completing this supplement, students will be able to:
1. Understand the principles of zero-sum, two-person games. 2. Analyze pure strategy games and use dominance to reduce the size of a game.
3. Solve mixed strategy games when there is no saddle point. SUPPLEMENT OUTLINE
M4.1
M4.2
M4.3
M4.4
M4.5
M4.6
Introduction
Language of Games
The Minimax Criterion
Pure Strategy Games
Mixed Strategy Games
Dominance
Summary • Glossary • Solved Problems • Self-Test • Discussion Questions and Problems • Bibliography
Appendix M4.1: Game Theory with QM for Windows
M4-1
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M4.1
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MODULE 4 • GAME THEORY
Introduction
In a zero-sum game, what is gained by one player is lost by the other.
M4.2
2/21/11
As discussed in Chapter 1, competition can be an important decision-making factor. The strategies taken by other organizations or individuals can dramatically affect the outcome of our decisions. In the automobile industry, for example, the strategies of competitors to introduce certain models with certain features can dramatically affect the profitability of other carmakers.
Today, business cannot make important decisions without considering what other organizations or individuals are doing or might do.
Game theory is one way to consider the impact of the strategies of others on our strategies and outcomes. A game is a contest involving two or more decision makers, each of whom wants to win. Game theory is the study of how optimal strategies are formulated in conflict.
The study of game theory dates back to 1944, when John von Neumann and Oscar Morgenstern published their classic book, Theory of Games and Economic Behavior.1 Since then, game theory has been used by army generals to plan war strategies, by union negotiators and managers
in
2/21/11
12:49 PM
Page M4-1
MODULE
4
Game Theory
LEARNING OBJECTIVES
After completing this supplement, students will be able to:
1. Understand the principles of zero-sum, two-person games. 2. Analyze pure strategy games and use dominance to reduce the size of a game.
3. Solve mixed strategy games when there is no saddle point. SUPPLEMENT OUTLINE
M4.1
M4.2
M4.3
M4.4
M4.5
M4.6
Introduction
Language of Games
The Minimax Criterion
Pure Strategy Games
Mixed Strategy Games
Dominance
Summary • Glossary • Solved Problems • Self-Test • Discussion Questions and Problems • Bibliography
Appendix M4.1: Game Theory with QM for Windows
M4-1
Z00_REND1011_11_SE_MOD4 PP3.QXD
M4-2
M4.1
12:49 PM
Page M4-2
MODULE 4 • GAME THEORY
Introduction
In a zero-sum game, what is gained by one player is lost by the other.
M4.2
2/21/11
As discussed in Chapter 1, competition can be an important decision-making factor. The strategies taken by other organizations or individuals can dramatically affect the outcome of our decisions. In the automobile industry, for example, the strategies of competitors to introduce certain models with certain features can dramatically affect the profitability of other carmakers.
Today, business cannot make important decisions without considering what other organizations or individuals are doing or might do.
Game theory is one way to consider the impact of the strategies of others on our strategies and outcomes. A game is a contest involving two or more decision makers, each of whom wants to win. Game theory is the study of how optimal strategies are formulated in conflict.
The study of game theory dates back to 1944, when John von Neumann and Oscar Morgenstern published their classic book, Theory of Games and Economic Behavior.1 Since then, game theory has been used by army generals to plan war strategies, by union negotiators and managers
in
Bibliography: Cambridge, MA: MIT Press, 1998. Halstead Press, 1978. Koselka, Rita. “Playing Poker with Craig McCaw,” Forbes (July 3, 1995): 62–64. Brandenburger, A., et al. “The Right Game: Use Game Theory to Shape Strategy,” Harvard Business Review (July–August 1995): 57—71. Lucas, W. “An Overview of the Mathematical Theory of Games,” Management Science 8, 5, Part II (January 1972): 3–19. Bushko, David, et al. “Consulting’s Future, Game Theory, and Storytelling,” Journal of Management Consulting (November 1997): 3. Luce, R. D., and H. Raiffa. Games and Decisions. New York: John Wiley & Sons, Inc., 1957. Davis, M. Game Theory: A Nontechnical Introduction. New York: Basic Books, Inc., 1970. Shubik, M. The Uses and Methods of Game Tlieory. New York: American Elsevier Publishing Company, 1957. Dixit, A. K., and Susan Skeath. Games of Strategy. New York; WW Norton and Co., 1999. Sinha, Arunava. “The Value Addition Game,” Business Today (February 7, 1998): 143. Dutta, Prajit. Strategies and Games: Theory and Practice. Cambridge, MA: MIT Press, 1999. Lan, Lim, et al. “Property Acquisition and Negotiation Styles,” Real Estate Finance (Spring 1998): 72.