## Differential Games in Economics and Management ScienceA comprehensive, self-contained survey of the theory and applications of differential games, one of the most commonly used tools for modelling and analysing economics and management problems which are characterised by both multiperiod and strategic decision making. Although no prior knowledge of game theory is required, a basic knowledge of linear algebra, ordinary differential equations, mathematical programming and probability theory is necessary. Part One presents the theory of differential games, starting with the basic concepts of game theory and going on to cover control theoretic models, Markovian equilibria with simultaneous play, differential games with hierarchical play, trigger strategy equilibria, differential games with special structures, and stochastic differential games. Part Two offers applications to capital accumulation games, industrial organization and oligopoly games, marketing, resources and environmental economics. |

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### Contents

I | viii |

II | xi |

III | 1 |

IV | 7 |

V | 9 |

VII | 13 |

VIII | 21 |

IX | 31 |

XLV | 195 |

XLVI | 196 |

XLVII | 197 |

XLVIII | 201 |

L | 226 |

LI | 236 |

LIII | 241 |

LIV | 243 |

X | 35 |

XI | 37 |

XIII | 41 |

XIV | 46 |

XV | 52 |

XVI | 58 |

XVII | 61 |

XVIII | 74 |

XIX | 79 |

XX | 80 |

XXI | 84 |

XXIII | 92 |

XXIV | 98 |

XXV | 106 |

XXVI | 107 |

XXVII | 109 |

XXIX | 113 |

XXX | 134 |

XXXI | 141 |

XXXII | 142 |

XXXIII | 144 |

XXXIV | 146 |

XXXVI | 153 |

XXXVII | 161 |

XXXVIII | 165 |

XXXIX | 168 |

XLI | 170 |

XLII | 171 |

XLIII | 187 |

XLIV | 194 |

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### Common terms and phrases

actions adjoint equation advertising assume assumption best reply brium capital stock chapter choose concave consider constant constraints control variables cost costate equations costate variables defined denote depend derive differential equation differential game Dockner dynamic game equilibrium strategies example feasible control path finite firm follower's follows game theory given Hamiltonian HJB equation holds implies infinite horizon leader linear quadratic Lipschitz continuous Markov perfect Nash Markovian Nash equilibrium Markovian strategies mode Nash equili noncooperative nondegenerate nondegenerate Markovian objective functional obtain open-loop Nash equilibrium open-loop strategies optimal control path optimal control problem optimal solution optimal value function output Pareto optimal payoff perfect Nash equilibrium profit quadratic differential resource right-hand side satisfied stationary Markovian Nash steady strategic form strategy profile subgame perfect switching symmetric system dynamics target path tion trajectory transversality condition trigger strategies utility function vector Wiener process yields zero