Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Games of skill
- 3 Games of chance
- 4 Sequential decision making and cooperative games of strategy
- 5 Two-person zero-sum games of strategy
- 6 Two-person mixed-motive games of strategy
- 7 Repeated games
- 8 Multi-person games, coalitions and power
- 9 A critique of game theory
- Appendix A Proof of the minimax theorem
- Appendix B Proof of Bayes's theorem
- Bibiliography
- Index
2 - Games of skill
Published online by Cambridge University Press: 02 December 2009
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Games of skill
- 3 Games of chance
- 4 Sequential decision making and cooperative games of strategy
- 5 Two-person zero-sum games of strategy
- 6 Two-person mixed-motive games of strategy
- 7 Repeated games
- 8 Multi-person games, coalitions and power
- 9 A critique of game theory
- Appendix A Proof of the minimax theorem
- Appendix B Proof of Bayes's theorem
- Bibiliography
- Index
Summary
It is not from the benevolence of the butcher, the brewer, or the baker, that we expect our dinner, but from their regard to their own interest.
Adam Smith 1789 ‘The Wealth of Nations’Games of skill are one-player games. Since they do not involve any other player, and when they involve nature it is under the condition of certainty, they are not really regarded as genuine games. Nature does not constitute a genuine second player, as in the case of games of chance, because nothing nature does affects the outcomes of the player's choices. The solitary player in games of skill knows for certain what the outcome of any choice will be. The player completely controls the outcomes. Solving a crossword puzzle is a game of skill, but playing golf is not, since the choices that the player makes do not lead to outcomes that are perfectly predictable. Golf is a game of chance involving uncertainty, although some would call it a form of moral effort! Nature influences the outcomes to an extent which depends on the player's skill, but the probability of which is not known.
The operation of single-player decision making is discussed in the following sections. The problem of linear programming and optimisation, where a player wishes to optimise some utility function within a set of constraints, is considered with the help of some realistic examples. The application of some basic concepts from calculus, including the Lagrange method of partial derivatives, is also discussed.
Linear programming, optimisation and basic calculus
The branch of mathematics known as linear programming or optimisation is devoted to games of skill.
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- Information
- Decision Making Using Game TheoryAn Introduction for Managers, pp. 17 - 31Publisher: Cambridge University PressPrint publication year: 2003