## Multiagent Systems: Algorithmic, Game-Theoretic, and Logical FoundationsMultiagent systems combine multiple autonomous entities, each having diverging interests or different information. This overview of the field offers a computer science perspective, but also draws on ideas from game theory, economics, operations research, logic, philosophy and linguistics. It will serve as a reference for researchers in each of these fields, and be used as a text for advanced undergraduate or graduate courses. The authors emphasize foundations to create a broad and rigorous treatment of their subject, with thorough presentations of distributed problem solving, game theory, multiagent communication and learning, social choice, mechanism design, auctions, cooperative game theory, and modal logics of knowledge and belief. For each topic, basic concepts are introduced, examples are given, proofs of key results are offered, and algorithmic considerations are examined. An appendix covers background material in probability theory, classical logic, Markov decision processes and mathematical programming. |

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### Contents

1 | |

19 | |

Games in Normal | 47 |

Computing Solution Concepts of NormalForm Games | 87 |

Reasoning and Computing with | 113 |

Beyond the Normal and Extensive | 141 |

Learning and Teaching | 189 |

Communication | 223 |

Mechanism Design | 261 |

Auctions | 315 |

An Introduction to Coalitional Game | 367 |

Logics of Knowledge and Belief | 393 |

Probability Dynamics and Intention | 421 |

A Probability Theory | 449 |

Markov Decision Problems MDPs | 455 |

473 | |

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achieve action proﬁle agents algorithm allocation Artiﬁcial Intelligence assignment assume axiom Bayesian game belief belief revision best response bidders chapter choose coalitional game computing congestion game consider constraint converge correlated equilibrium deﬁned Deﬁnition denote discussed distribution dominant strategies dominant-strategy efﬁcient equilibrium strategy example exists expected utility extensive-form game f f f Figure ﬁnd ﬁnding ﬁnite ﬁrst ﬁrst-price auction game G game theory given graph Groves mechanisms inﬁnite information set Intuitively iteration knowledge learning linear program matching maximize maxmin mechanism design minmax mixed strategy mixed-strategy modal logic multiagent Nash equilibrium node Nogood normal-form game optimal outcomes payment perfect-information play player 1’s polynomial possible preferences probability problem properties pure strategy quasilinear repeated game replicator dynamic representation require robot rule satisﬁes second-price auction Section sequence Shapley value social choice function solution concepts speciﬁc stochastic games strategy proﬁle Theorem two-player utility function valuation variables voting