Decision Making using Game Theory An introduction for managers 1st Edition by Anthony Kelly ISBN 9780511058615 0511058616

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Product details:
ISBN 10: 0511058616
ISBN 13: 9780511058615
Author: Anthony Kelly

Decision Making using Game Theory An introduction for managers 1st Edition Table of contents:

1 Introduction

Terminology

Classifying games

A brief history of game theory

Layout

2 Games of skill

Linear programming, optimisation and basic calculus

The Lagrange method of partial derivatives

3 Games of chance

An introduction to basic probability theory

Expected value, variance and standard deviation

Games of chance involving risk

Utility theory

Games of chance involving uncertainty

4 Sequential decision making and cooperative games of strategy

Representing sequential decision making

Sequential decision making in single-player games

Sequential decision making in single-player games involving uncertainty

Sequential decision making in two-player and multi-player games

Cooperative two-person games

Purely cooperative games

Minimal social situation games

5 Two-person zero-sum games of strategy

Representing zero-sum games

Games with saddle points

Dominance and inadmissibility in large saddle point games

Games with no saddle points

Large matrices generally

Interval and ordinal scales for pay-offs

Games with ordinal pay-offs and saddle points

Games with ordinal pay-offs, but without saddle points

6 Two-person mixed-motive games of strategy

Representing mixed-motive games and the Nash equilibrium

Mixed-motive games without single equilibrium points: archetype 1 – leadership games

Mixed-motive games without single equilibrium points: archetype 2 – heroic games

Mixed-motive games without single equilibrium points: archetype 3 – exploitation games

Mixed-motive games without single equilibrium points: archetype 4 – martyrdom games

Summary of features of mixed-motive prototypes

Leadership games

Heroic games

Exploitation games

Martyrdom games

The Cournot, von Stackelberg and Bertrand duopolies: an interesting application of mixed-motive game

The Cournot duopoly

The von Stackelberg duopoly

The Bertrand duopoly

Solving games without Nash equilibrium points using mixed strategies

7 Repeated games

Infinitely repeated games

Finitely repeated games

Backward induction and its inherent paradox

Avoiding the paradox of backward induction: bounded rationality

Avoiding the paradox of backward induction: multiple Nash equilibria

Avoiding the paradox of backward induction: uncertainty

Avoiding the paradox of backward induction: incomplete information

8 Multi-person games, coalitions and power

Non-cooperative multi-person games

Mixed-motive multi-person games

Partially cooperative multi-person games

Indices of power: measuring influence

Underlying assumptions: sincerity, completeness and transitivity

The Shapley value

The Shapley–Shubik index

An analysis of power on ‘voluntary maintained’ boards (Model A)

Three-faction coalitions

Four-faction coalitions

Grand coalitions

The Shapley value for each faction

The Shapley–Shubik index for each faction

An analysis of power on ‘controlled secondary’ boards (Model B)

Two-faction coalitions

Three-faction coalitions

Grand coalitions

The Shapley value for each faction

The Shapley–Shubik index for each faction

An analysis of power on out-of-state boards (Model C)

Three-faction coalitions

Four-faction coalitions

Grand coalitions

The Shapley value for each faction

The Shapley–Shubik index for each faction

Conclusions

The relative power of major and minor players

The relative power of the minor players

The pay-off for winning coalitions

The order of voting or coalescence

Minimal winning coalitions

Other applications

Implications for forming committees

The Johnston index

The Deegan–Packel index

The Banzhaf index

Summary

9 A critique of game theory

Rationality

Indeterminacy

Inconsistency

Conclusion

A Proof of the minimax theorem

Preamble

Proof: step 1

A graphic model for the game

Proof: step 2

Proof: step 3

Proof: step 4

Proof: step 5

B Proof of Bayes’s theorem

Preamble

Proof

Bibliography

Index

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