## Games and Decisions: Introduction and Critical Survey"The best book available for non-mathematicians." — Contemporary Psychology.This book represents the earliest clear, detailed, precise exposition of the central ideas and results of game theory and related decision-making models — unencumbered by technical mathematical details. It offers a comprehensive, time-tested conceptual introduction, with a social science orientation, to a complex of ideas related to game theory including decision theory, modern utility theory, the theory of statistical decisions, and the theory of social welfare functions. The first three chapters provide a general introduction to the theory of games including utility theory. Chapter 4 treats two-person, zero-sum games. Chapters 5 and 6 treat two-person, nonzero-sum games and concepts developed in an attempt to meet some of the deficiencies in the von Neumann-Morgenstern theory. Chapters 7–12 treat n-person games beginning with the von Neumann-Morgenstern theory and reaching into many newer developments. The last two chapters, 13 and 14, discuss individual and group decision making. Eight helpful appendixes present proofs of the famous minimax theorem, several geometric interpretations of two-person zero-sum games, solution procedures, infinite games, sequential compounding of games, and linear programming.Thought-provoking and clearly expressed, Games and Decisions: Introduction and Critical Survey is designed for the non-mathematician and requires no advanced mathematical training. It will be welcomed by economists concerned with economic theory, political scientists and sociologists dealing with conflict of interest, experimental psychologists studying decision making, management scientists, philosophers, statisticians, and a wide range of other decision-makers. It will likewise be indispensable for students in courses in the mathematical theory of games and linear programming. |

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### Contents

CHAPTER | 1 |

Utility Theory I | 12 |

Extensive and Normal Forms | 39 |

TwoPerson ZeroSum Games | 56 |

APPENDICES | 81 |

TwoPerson NonZeroSum NonCooperative | 88 |

TwoPerson Cooperative Games II 4 | 114 |

TwoPERSON GAMES | 145 |

CHECKING ALL CRITICAL POINTs | 426 |

THE Double DESCRIPTION METHOD | 430 |

THE SIMPLEx METHOD | 432 |

A GEOMETRIC INTERPRETATION OF THE SIMPLEX AND DUAL SIMPLEX PROCEDURES | 435 |

DIFFERENTIAL EQUATION solutions of SYMMETRIC GAMEs | 438 |

SYMMETRIZATION OF A GAME | 440 |

ITERATIVE solution of GAMES BY FICTITIOUS PLAY | 442 |

Games with Infinite Pure Strategy Sets | 447 |

Theories of nPerson Games in Normal Form I 55 | 155 |

Characteristic Functions | 180 |

Solutions | 199 |

Io WStability | 220 |

Applications of nPerson Theory | 253 |

Individual Decision Making under Uncertainty | 275 |

Group Decision Making | 327 |

APPENDICES | 371 |

THE UTILITY AND subjecTIVE PROBABILITY FUNCTIONs | 378 |

The Minimax Theorem | 385 |

First Geometrical Interpretation of a TwoPerson | 394 |

Second Geometrical Interpretation of a TwoPerson | 400 |

Linear Programing and TwoPerson ZeroSum | 408 |

REDUCTION OF A LINEARPROGRAMING PROBLEM TO A GAME | 419 |

Solving TwoPerson ZeroSum Games | 424 |

TRIAL AND ERROR | 425 |

GAMEs witH NovaLUE | 448 |

GAMEs where A or B Is FINITE | 450 |

GAMEs where A is ALMost FINITE | 451 |

GAMES INvolving TIMING or PARTITIONING | 453 |

A MODEL of PokeR DUE TO Borel | 456 |

Sequential Compounding of TwoPerson Games | 457 |

STOCHASTIC GAMEs | 458 |

RECURSIVE GAMES | 461 |

GAMES OF SURVIVAL | 467 |

MULTICOMPONENT ATTRITION GAMEs | 476 |

APPROACHABILITYEXCLUDABILITY THEORY AND COMPOUND DECISION PROBLEMs | 479 |

Dividend Policy AND ECONOMIG RUIN GAMEs | 483 |

485 | |

501 | |

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Games and Decisions: Introduction and Critical Survey R. Duncan Luce,Howard Raiffa Limited preview - 2012 |

### Common terms and phrases

alternatives analysis arbitrated solution arbitration scheme argument assumed assumption axioms Chapter characteristic function choose coalition structure collusion concept condition conflict of interest consider constant-sum cooperative game decision denote discussion dominates economic equilibrium pairs equilibrium point equilibrium strategy example exists expected value extensive form finite number gamble game in extensive game theory game tree given imputations indifferent individual information sets interpersonal comparisons least linear utility function lottery mathematical maximin strategy maximize minimax theorem mixed strategy move n-person games n-tuple Nash Nash's negotiation set Neumann and Morgenstern non-cooperative game normal form notion outcome Pareto optimal payoff matrix play player 1’s player 2's possible preplay communication pure strategy rational reasonable restricted security level sense Shapley Shapley value side payments situation social strategy choice strategy x strictly competitive games subset theorem theory of games tion tive two-person games two-person theory unique utility theory yield zero-sum game