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On Existence, Mixtures, Computation and Efficiency in Multi-objective Games

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PRIMA 2018: Principles and Practice of Multi-Agent Systems (PRIMA 2018)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11224))

Abstract

In a multi-objective game, each individual’s payoff is a vector-valued function of everyone’s actions. Under such vectorial payoffs, Pareto-efficiency is used to formulate each individual’s best-response condition, inducing Pareto-Nash equilibria as the fundamental solution concept. In this work, we follow a classical game-theoretic agenda to study equilibria. Firstly, we show in several ways that numerous pure-strategy Pareto-Nash equilibria exist. Secondly, we propose a more consistent extension to mixed-strategy equilibria. Thirdly, we introduce a measurement of the efficiency of multiple objectives games, which purpose is to keep the information on each objective: the multi-objective coordination ratio. Finally, we provide algorithms that compute Pareto-Nash equilibria and that compute or approximate the multi-objective coordination ratio.

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Notes

  1. 1.

    Tobacco consumers are free to value and choose cigarettes how it pleases them. However, is value the same when they inhale, as when they die suffocating?

  2. 2.

    It is a backtrack from the subjective theory of value, which typically aggregates values on each objective/commodity into a single scalar by using an utility function.

  3. 3.

    All the proofs are in the long paper on arxiv.

  4. 4.

    In the single-objective case, Pareto-Nash and Nash equilibria coincide.

  5. 5.

    In a finite multi-objective game, sets N, \(\{A^{i}\}_{i\in N}\) and \({\mathcal {D}}\) are finite.

  6. 6.

    To enumerate the number of ways to distribute number n of symmetric agents into \(\alpha \) parts, one enumerates the ways to choose \(\alpha -1\) “separators” in \(n+\alpha -1\) elements.

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Authors and Affiliations

  1. RIKEN, Center for Advanced Intelligence Project AIP, Tokyo, Japan

    Anisse Ismaili

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  1. Anisse Ismaili
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Correspondence to Anisse Ismaili .

Editor information

Editors and Affiliations

  1. School of Computing and Information Systems, University of Melbourne, Melbourne, Australia

    Tim Miller

  2. Department of Computer Science, University of Aberdeen, Aberdeen, UK

    Nir Oren

  3. Artificial Intelligence Research Center (AIRC), National Institute of Advanced Industrial Science and Technology (AIST), Tokyo, Japan

    Yuko Sakurai

  4. Artificial Intelligence Research Center (AIRC), National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Japan

    Itsuki Noda

  5. University of Otago, Dunedin, New Zealand

    Bastin Tony Roy Savarimuthu

  6. Computer Science Department, New Mexico State University, Las Cruces, USA

    Tran Cao Son

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Ismaili, A. (2018). On Existence, Mixtures, Computation and Efficiency in Multi-objective Games. In: Miller, T., Oren, N., Sakurai, Y., Noda, I., Savarimuthu, B.T.R., Cao Son, T. (eds) PRIMA 2018: Principles and Practice of Multi-Agent Systems. PRIMA 2018. Lecture Notes in Computer Science(), vol 11224. Springer, Cham. https://doi.org/10.1007/978-3-030-03098-8_13

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  • DOI: https://doi.org/10.1007/978-3-030-03098-8_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-03097-1

  • Online ISBN: 978-3-030-03098-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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