Cover -- Half-title -- Title -- Copyright -- Contents -- Preface -- 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 games -- 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.