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Reciprocation Effort Games

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Artificial Intelligence (BNAIC 2017)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 823))

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Abstract

Consider people dividing their time and effort between friends, interest clubs, and reading seminars. These are all reciprocal interactions, and the reciprocal processes determine the utilities of the agents from these interactions. To advise on efficient effort division, we determine the existence and efficiency of the Nash equilibria of the game of allocating effort to such projects. When no minimum effort is required to receive reciprocation, an equilibrium always exists, and if acting is either easy to everyone, or hard to everyone, then every equilibrium is socially optimal. If a minimal effort is needed to participate, we prove that not contributing at all is an equilibrium, and for two agents, also a socially optimal equilibrium can be found. Next, we extend the model, assuming that the need to react requires more than the agents can contribute to acting, rendering the reciprocation imperfect. We prove that even then, each interaction converges and the corresponding game has an equilibrium.

G. Polevoy—Most of this work was done at Delft University of Technology.

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Notes

  1. 1.

    A combination is convex if it has nonnegative weights that sum up to 1.

  2. 2.

    Contributions by default refer to the contributions at time zero.

  3. 3.

    \(\beta _i > 1\) implies negative utilities that sometimes result in negative \({{\mathrm{PoA}}}\) and \({{\mathrm{PoS}}}\).

  4. 4.

    The actual limit does not have to be zero; zero is just the result from the contradictory assumption.

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Acknowledgments

We thank Prof. Orr M. Shalit from the Technion, Israel for the useful discussions. This work has been supported by SHINE, the flagship project of DIRECT (Delft Institute for Research on ICT at the TU Delft).

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Authors and Affiliations

  1. University of Amsterdam, Amsterdam, The Netherlands

    Gleb Polevoy

  2. Delft University of Technology, Delft, The Netherlands

    Mathijs de Weerdt

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  1. Gleb Polevoy
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  2. Mathijs de Weerdt
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Correspondence to Gleb Polevoy .

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Editors and Affiliations

  1. Artificial Intelligence, University of Groningen, Groningen, The Netherlands

    Bart Verheij

  2. Artificial Intelligence, University of Groningen, Groningen, The Netherlands

    Marco Wiering

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Polevoy, G., de Weerdt, M. (2018). Reciprocation Effort Games. In: Verheij, B., Wiering, M. (eds) Artificial Intelligence. BNAIC 2017. Communications in Computer and Information Science, vol 823. Springer, Cham. https://doi.org/10.1007/978-3-319-76892-2_4

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  • DOI: https://doi.org/10.1007/978-3-319-76892-2_4

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